How could a young man avoid the draft during the Vietnam Era?
You could move abroad
Some young men became expatriates in order to avoid the draft.
Some men familiarized themselves with the loopholes.
Many successful strategies for avoiding the draft involved staying in college (Newt Gingrich gamed this strategy), being the primary source of income for a large family (Billy Joel used this one), feigning illness or disability (Donald Trump used this), claiming to have used LSD and other drugs (Ted Nugent, in some interviews, claimed to have done this but denied it later), and claiming to be a homosexual.
Some fled to Canada. Some claimed to be conscientious objectors for religious or moral reasons. Possibly, some claimed membership in the Communist Party. Others avoided the draft by joining the state-level National Guard (including Dan Quayle, George W. Bush and Bill Clinton).
Not all of these strategies worked for everyone who tried them, but most of them worked for somebody at some point.,