I grew up in the 80s rather than the 60s, but there weren't any comic shops then either (at least not in my area). There was one periodicals shop in town, but it was mostly about magazines and only had a limited comics section.
Many of my comics came from flea markets and the like, I would look for someone with a box of loose comics for around 10 to 25 cents each and buy a bunch.
Another big source for me was a local family owned conveience store, they had a spinner rack full of coverless comics for 15 cents (later raised to 25). I thought it strange that a retail store would be selling apparently used comics, but they were cheap and I was broke, so I really didn't care. It wasn't until many years later that I learned of the shady practice of taking the covers off comics/magazines/novels, sending those back to the publisher and claiming the books were destroyed, just to turn around and sell them at a discounted price.
Then there was a periodicals store (something of a precursor to the dedicated comic shops) with a moderate selection of comics. I got quite a few new ones there, right at the time when comics were shifting from 75 cents to a dollar.
I also got quite a few in those deals where you get a bag of 3-5 overstock comics for a couple bucks, and a bunch of comics during a school carnival. I sucked at the games, but I did have a bunch of game tickets and knew a couple kids who loved to play the games and didn't care about the prizes, so I gave them tickets to play and they gave me the comics they won. I got a bunch of transformers comics that way, plus some archie, sectuars, and a few others.