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 )