I got my phones off of Seoul Craigslist. Just browsed around for a good price, messaged a few sellers, negotiated it down a little, and then arranged to meet up (in a very public place in broad daylight!!) to get the phone. You should make sure and ask before you buy it that the phone is in fact unlocked, and that it can be used with any carrier.
After that, I just took the phone to the big global Olleh store in Hongdae (most little neighborhood Olleh stores are not going to do this; you have to go to a big branch) and bought a SIM card, then got set-up on a prepaid data / calls / text plan. They put the SIM card in for me and then I just had to wait about an hour before everything was activated and ready to go. One time I went, there was a worker who spoke excellent English and it was all easy peasy. But the other 6+ times I went to refill my minutes, that was not the case and I had to do everything in Korean. So if you can, bringing someone who speaks Korean with you (unless you do!) will be extremely helpful and make the whole process much less painless. 선불 is the word for prepaid in Korean, btw. That’ll be important.
There are stores in Itaewon where you can buy used phones as well, but I went once with a friend and it was a genuinely TERRIBLE experience. The guys running the shop were obvious sleezeballs intent on ripping us off, and the whole thing took 3+ hours, and we were just really uncomfortable the whole time. SO unless you know of a reputable shop, I don’t really recommend just walking into any used phone store you see because chances are you will get screwed over. :| At least online, you can pick your price and know exactly what you’re paying and compare it to other sellers, where as a lot of these privately-owned phone stores will tack on random last-minute fees and try to scam you.