The slightly longer answer: unless there is a serious national emergency, and you happen to turn 20 the year the draft is invoked, and you are male, and you are not gay or bisexual, and you don't manage to get an exemption as a conscientious objector. There are other holes, but those are the main ones.
A more complete answer:
Selective Service. What a euphamism.
Things have changed a lot since the Vietnam draft. The draft selection algorithm is different now, and it is supposedly more difficult to get an exemption from service. Not impossible, though.
If the President ever approves a draft, Selective Service will randomly select the desired quantity of conscripts from the set of eligible registered men who turned 20 the year of the draft. I am not certain of the exact boundary conditions. In the extremely unlikely event that this pool of individuals is exhausted (overzealous use of cannon fodder, perhaps), Selective Service will move on to age 21, age 22, and so forth. Once you turn 26, you are no longer eligible to be drafted. Of course if the Selective Service system ever gets that far, we're probably in some sort of cataclysmic war where we're all screwed anyway.
There are two types of conscientious objectors who may be excused from service. Some people have a strong objection to bearing arms, but might be able to serve the military in other ways. These people will likely find themselves at military desk jobs, transporting supplies, and so forth, but will not be asked to use weapons in any way. Note that supply convoys are popular targets, so this route does not guarantee safety. Others are completely unwilling to serve the military, and these people may be asked to spend an equivalent amount of time performing some peaceful job that benefits the community.
It is not particularly easy to gain conscientious objector status. Generally the draft board will be interested in the details of your beliefs and their origins. Letters from friends, relatives, and religious figures and other documentation of your pre-existing anti-war lifestyle are likely to help convince the board.
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