The principle of a rebound is that you lead a direction, then change your mind, either half way, or right at the end, in order to come back. Of course, you never "change your mind", you plan it all along and let your partner know about it in good time. How you do that? Simple. You lead the first direction, but as soon as your partner gets it, you lead the opposite. That way, by the time she gets to the first half of the beat, she already knows where you need her to be next.
Now, suppose you want to push this further - go one direction, then back, then change your mind again. Since the direction at the start of the movement is the same as at the end of the movement, there is no point leading the opposite direction at all, because nobody is going there. If you're in a car and you lead the backward direction, but in the end still go forward, how do you call that? A break! That's what you do here, also: you break the movement.
And you can break it more than once, during one movement. The point is that, while you release the break, you need to show your partner what comes next: another break, or a continuation. You do that in a variety of ways, two being the most notable in my humble opinion:
1. the freedom you give your partner to release the energy from the break and
2. the counter-position: you achieve the break with a counter-position, but the release is also a counter-position. The acceleration pedal is a force inflicted on the car, just as the break pedal - except you usually decide to follow-up on the acceleration pedal; however, if you decide not to, to push the two pedals alternately, you achieve a series of counter-positions which are quite clear to your partner. Something like the ABS.
But let's take the trick up a notch: reach an "American" position, then lead your partner a gancho to your forward leg and try to keep her there for a second, chained, gancho; then lead her an exit to a back ocho. ;)

Take a simple exercise as a base step - leader takes a right step forward on the outside (open side of the embrace), then collects feet and changes weight at the same time; leader takes a right step back then collects feet and changes weight. That's it. Do it first on the beat, then on double beat. Chain two sequences on double beat, if you feel it in the music - but always complete any single sequence at the same speed, don't break it in the middle.

It is very important for the leader to learn how to lead the start and and the end of a double beat sequence (the middle part comes more naturally). An option which is not full-heartedly endorsed by most teachers is to give the follower a lifting sensation at the start of a fast sequence and a grounding sensation at the end (or just lose the lifting sensation :P ).

Having prepared these details, here is a small brief of musicality for any regular Milonga music:

• Milonga is made up of phrases of eight beats. You can imagine a musical phrase as a text, beginning with a capital letter, and ending with a full stop. Then the next phrase tells something different. In the music, you will usually notice that different instruments in the orchestra will start or stop playing when a new phrase begins. What is important for the dance is - you want to start a sequence when a phrase starts and end a sequence when a phrase ends. You don't want a phrase to start, catching you in the middle of a sequence. It looks bad. It looks particularly bad if you are still dancing when the music stopped completely.
• Coming back to the little exercise - suppose you do it on the beat (which is called Milonga lisa). Then, you may want to make your first step (right forward as a leader) on the beats one or five of each phrase, because, as you will notice, the music places a particular accent on those beats. The typical tango orchestra has a special instrument called the bandoneon. This instrument, much like the classical accordion, plays both during compression and expansion, but it plays stronger during compression, which normally happens on beats one and five, hence the accents
• Now, suppose you do the little exercise on double beat as well (which is called Milonga doble tiempo) - and then try to go back to normal beat. You will notice that you can become "off-phase" with the previously explained idea. Depending on how many "doble tiempos" you did, you can be off phase in two ways, depending on which beat your forward step falls. If it falls on beat four, you can do a half rebound, in double time, which will put you back on the track; if it falls on beat three, you can do a second step forward, instead of the step back.
• The third possible way to dance Milonga is called Milonga con traspie (which means "stumble"). If you listen to some Milonga music, you will notice that it has an "exposition" part, at the beginning, which gives away some of the theme (and also gives time to the leaders to invite their partners on the dance floor), then there is a clear statement of the essential Milonga rhythm (In fact, a clear statement of the candombe rhythm which survived inside the common modern Milonga). This piece of music will then accompany the whole tune, so you'd better get accustomed to it. Dancing to that piece is in fact doing the Milonga con traspie. And to do it you need to start on the end of an even beat (preferably four or eight), do a syncope, then a doble tiempo (and, if you feel like it, repeat). A few words about a syncope: take one beat, split it in four, wait for three quarters of it (poised, like a tiger), then step on the last quarter. So, a traspie step would be something like: 4(step), 4+1q(wait), 4+2q(wait - tiger like attitude), 4+3q(step), 5(step), 5+1h(step), 6(step). While that is a rather sterile mathematical explanation (mind you some of these are quite useful: I make my tie knots by such a formula :D ) - catching the piece of music that gives the traspie is infinitely more important for you (hint: it's like "ta-dam tam tam, ta-dam tam tam"... and I can keep doing that :P )

(Notes from a splendid lesson by Murat Elmadağlı (Turkey) & Vera Gogoleva (Russia))

Having just returned from TangON, with a wealth of news in my head and a misplaced notebook, I'm quite likely to just rush a sum of words with minimum sense - but I'll do it anyway, counting on my faithful correspondents to help me trace their heads and tails.

• The close embrace (Pablo & Noelia) - the right arm should delimit the couple's space, so in a sense, it is the reference of the leader with respect to the environment. Therefore, it should maintain a rather rigid vertical attitude relative to the movement, instead of leaning inside and outside when the follower's position shifts or twists. The hand's place can be more or less mobile however
• Contretiempo (Chicho) - ... is a step which is either lead to the follower and not followed by the leader, or the other way around. Reading back that sentence, I conclude that 1) I like it, it's smart and 2) it looks like a philosophical egg with a tail. So, let me explain it: many times, there is a symmetry between the leader's steps and the follower's, much like a mirror. That way, the pair stays close (e.g. in straight forward movement). But the leader doesn't lead with his feet, so one should find it possible to lead a step without moving their own feet, or move their feet without actually leading anything (or leading something which is not symmetrical with their movement). While the latter is usually easy, the former is much, much more subtle.
  As an example, try the following exercise: lead a sidestep,change of weight, then another sidestep in the same direction to your partner, while doing the same thing. Easy. Now, lead the same, but skip your change of weight, simply do a forward step, to the sidestep direction, while remaining twisted towards your partner. Your step is easy, her step is equally easy, but leading it can be quite tricky. Don't use your hands. A 'mystical' explanation says use your breath instead. Lead her a slight up/down movement, which is trick for 'step and collect', because it feels the same. Keep in mind that, even when done perfectly, there's a chance she will miss it, so prepare for that.
  A more advanced exercise: start with a back ocho; on the movement to your right, play a barida to her left foot, as if you would start a sanguchito, but instead, lead her the step back, change of weight and forward, in double time, on your right side. Don't do the change of weight, rebound to your left foot instead (you can do an adorno to keep track of time ;) ), then, while she steps forward and forward again, you cross twice in double time. At the end of this sequence, you will find yourself in a good position to lead her a stop signal and do a gancho to her left foot (which, if you are smart, you won't do).
• Giro without torsion (Damian & Celine, Sebastian & Mariana) - I'll try to summarize my take on the milonga workshops in several notes. The first two points are twin: 1) there is no time for the regular steps & torsion in the milonga tempo; and 2) it's very important that you take your time to do the steps, instead of making / leading them faster than they actually are. So the steps need to be very small and you will want to lead them in close embrace, to save time on the "communication" process. You will also want to cut corners - for instance, an ocho, which is usually done by pivoting the follower, will be done faster by simply crossing (behind or forward). Similarly, a linear giro will be done by leading a back cross (push the follower slightly away then pull her back shifted over her weight foot), to indicate the direction of the first step, while pitching to the direction where you want the giro to go. That is, of course, if you have enough space on the floor to do that. Which you normally don't. So you can evolve this into a normal giro, which is circular (as the name tends to indicate), therefore needs some torsion. Still, instead of actually twisting your torso, as you might normally do, all you need in order to get the job done is to twist your hips - and only just. Arguably (imho) this can be achieved better if the leader's right hand stays fixed under the follower's right arm, instead of sliding on her back, during the twisting moves. Not very comfortable at first, but it kind of grows on you. as a neat trick, lead a giro with all steps in double time, very small steps, and perform the same steps, mirrored. If done right, this is called a 'corelita'.
• Movement (Pablo & Noelia) - a very simple, but very important note: when you move, concentrate on the foot holding the weight, not on the free foot. The movement itself comes from the horizontal push into the pivot foot, that particular force is the vector, not the free foot pointing, or the mere inertia. This helps balance a lot, and allows the leader to plan respect the paradigm of leading: lead, check, then follow (i.e. as opposed to lead, step simultaneously and hope for the best)

Try this simple exercise:

1. Stand on both your feet, as you normally do when not walking.
2. Now, keeping your body straight, try to lean very slightly to your front, as much as your feet allow it without having to make a step. You should now feel your weight resting on your toes.
3. Now, lean as much as you can towards your back. Remember, your body should not bend in any way. You should now feel your entire weight on your heels.

Maintaining your axis is a very important thing when dancing tango. In fact, you should probably concentrate most of your attention in the beginning on how to step and how to pivot while keeping your wight on the right foot.
You wouldn't want to push or pull your partner and you wouldn't want him/her to feel as trying to move a door!

This is the beauty of it all when speaking about axis. You can lean on your toes and give him/her that perfect embrace he/she's been longing for and still allow your legs to have enough room in order to make the steps, the pivots and those nice adornos you've been admiring on YouTube.
Or you can simply lean towards your back to magnify your steps, to better feel the energy and put it into your best moves.

Now don't misunderstand! During a single song, you will probably switch between the two depending on where he may lead and on how she may want to shape it. The important thing is to keep in mind that between your toes and your heels is the place you want to keep your weight and your axis. Also remember that your partner has the same range to play with when it comes to his/her axis. Therefore, the most beautiful movements will probably derive from this game you are both playing.

There will be times when you will feel that you have pushed out of this range and lose your balance. Even if this is acceptable for the first few lessons, in time, you should learn to control your body as you please! "Really?" you may ask. Well, in fact, yes! After all, it is YOUR body we are speaking of and YOU of all people should be able to control it as you please. Yes, you may lose your balance. And yes, you may not be able to make that perfect pivot from the very first lesson. But that is all probably because nobody has really explained you how to do it. In your own terms.

The key to keeping your axis is the perfect balance between the energy you are receiving and the steps you are making (together with the shape you decide to give them). For example, when talking about a voleo, you can actually pinpoint the energy rising from the leader's torso, going through his arms into the follower's arms, upper body, leg and finally all the way through to her toes, giving the beautiful shape of a voleo.

What kind of exercises can you try for maintaining your axis?

Caminar - maintain at every step your toes, your torso and your forehead on the same vertical line.
Caminar with a counter balance - work in pairs. When you are walking to the front, your partner should push you to the back. You should be able to push him back and make a step in perfect balance. When you are walking to the back, your partner should push you forward. Work until you can make steps in perfect balance. You should be able to do that by finding the equilibrium between the energy of your partner's push and the energy you invest in the movement.
Pivot to the wall - take the wall as your partner and try to make 180 degrees pivots in perfect balance. At first, you will lean towards the wall to take the energy you need. In time, you should be able to let it go more and more and finally, do the pivots on your own. After that, play with the speed of the pivots and the adornos you can do.

Here are the first 10 hints:
/TODO/ Intro ...

1. It's more about listening than it is about dancing.
2. There are three steps (just three): forwards, backwards and sideways.
3. There are two roles: leader and follower.
4. There are three Tango rhythms: the Tango (classical), the Milonga and the Tango Waltz; the "New Tango" or "Tango Nuevo" can also be seen as a separate branch.
5. Tango is usually danced in a ring, following (and respecting) a counter clockwise direction.
6. The embrace is arguably the most important feature of the dance. It can be open or closed.
7. Most of the time, Tango dancers have all their weight on one foot, whose choice is not (entirely) random.
8. There is (surprisingly) such a thing as a "basic step", or "basico".
9. There are two dancing systems - parallel and crossed.
10. There are many great teachers of Tango touring the world, from which you can learn new tricks.

And now the explanations: