Verified answer

Why do you think they all did the exact same thing? Some went straight away. Some went as a last resort. There was no guidebook to draft dodging that draft dodgers conformed to. 

A draft dodger in my hometown tried going to college, but flunked out, then tried to get a doctor's letter, but couldn't, then as his number quickly approached, resorted to burning down the courthouse because that's where the local draft records and birth certificates were all kept, not realizing that the state and federal government also had copies, so he ended up fleeing to Canada not just because he was dodging the draft but because he was fleeing arrest for burning the 150-year-old historic courthouse right down to the ground. 

I won't say that no good came of the situation though, as I do have a rather glorious picture in my living room of the courthouse burning down in middle of the night. My mom and aunt also said that word got out and most the guys of draft age ended up going to watch it burn down, and girls of course too, which is why my mom and aunt went down there to see it, along with their boyfriends. And all those hordes of teenagers and early twenty-somethings cheered as it burned and booed at the firemen in the wee hours until after the sun came up and all that was left was a giant, smoldering hole in the ground where the courthouse used to be.

There weren't that many who really went to Canada.  Student deferments were available until 1970 or so.  Medical deferments ( like the one Pres. Trump got) were an option.  Once a draft notice was received, it would take the draft board  some time to figure out who the non-responders were and when to notify law enforcing. If someone was intent on avoiding the draft, they probably didn't register and that would take even longer to figure out  ( there were few computers in use) 

It was kind of a slow motion process, with appeals and evasion was possible as people were harder to track in those days.  

The guys who went to Canada were usually those who were tired of the appeals, hiding etc and wanted to take the pressure off themselves. 

Draftees usually ended up in Infantry, which was taking high casualties  from 1967-1972.   

depended.  I'm told that, before the draft lottery was instituted, a dodger would leave as soon as he received notice he had been reclassified "1-A' and after the lottery, he'd go as soon as he knew his lottery number was low enough that he'd likely be called up to serve.  don't for sure know as I flunked the Army physical myself due to coke bottle thick glasses [if you know what a coke bottle was].  -- grampa

What the Anon said. 

Carter pardoned them in 1977. One third, who had created successful lives in Canada remained living there although most did return for visits.

I would have been a conscientious objector and accepted my prison term.  Trump bribed a doctor to say he had bone spurs while Clinton found other means to avoid going to Vietnam.

Those without connections or money tried other means to stay out of the war, which by all accounts was hell for all those who did have to go.

We should abolish drafts.