Be an officer.
You see, when they draft you they can do whatever they want with you. In less than a month you could be on the battlefield, holding a gun, and trying to kill someone who you don't know. If, instead, you sign up as an officer, they are willing to go to a lot of effort to train you (and this training takes place on United States soil - probably a pretty safe place). Then, if the war isn't over by the time you are fully trained, you are less likely to be sent to the front lines as cannon fodder, because the military isn't too into killing people who they just spent a lot of money training. In the sixties this led to a lot of people joining ROTC after draft numbers were assigned. Once a person found out that they had a draft number of, say, 3 (very bad) they might try to join ROTC.
An interesting side effect of this was that the military's general political stance, not the "official military political stance" - there isn't one of those - but the political stance of the average military officer, moved significantly to the left in the period during and for a few decades following the Vietnam War (note this is all relative. They moved left from a very conservative average - it is possible that they almost got to a centrist stance). Many people had joined as a draft dodging effort and after their four years of ROTC paypack found that they either enjoyed the work or were quite good at it, and stayed in. Recently this generation of soldiers has been retiring and the military's politics have swung back to the right. Whether it is a good thing to have a military whose opinions represent only a part of the population they defend is an issue of debate.
Unfortunately this trick only works for people who are both in college and fit/smart enough to join ROTC, which means that poor and/or stupid people are much more likely to be sent to the front lines, because they don't have this trick available. Whether killing the poor and stupid disproportionately is a good thing or not is left as a debate between the social darwinists and liberals.
Note that this is but one way to dodge the draft. Others include the legal ones such as "plead pacifism and go to jail instead", "successfully become a conscientious objector" (usually only available for religious reasons), and the illegal "go to Canada". Whatever you do, if there is a draft, make sure you know all your options. I can imagine no worse fate than to be forced to die for a cause I don't believe in. On the other hand, part of the reason we created this "more perfect union" was to provide for the common defense. Whatever you decide, the goal here is to make it your decision. Good luck, let's hope this advice remains irrelevant.
NotFabio points out that one must be very very careful with this approach. When you become an officer you can be recalled into active duty at any time, and you must keep track of your papers, because the military is historically very bad at doing so when it would be disadvantageous to them. This is all about weighing the pros and cons of each approach: 2 to 4 years of indentured sucky servitude, or a potential lifetime to less sucky service.