I've done self-driving in jeju for 4days back in 2011. Here's my experience:
1) didn't book online because I've read somewhere it's cheaper to rent from local rental company and you might get eng gps if lucky. After arriving, there was a stretch of car rental booths. I just went to the cheapest one. Unfortunately, I couldn't remembered the name. All I've remembered is it's green color and looks very local.
2) I just filled up some forms and the staffs directed me to take shuttle bus to their company actual site. Unfortunately, the staff at the actual site does not speak any eng. And my friend and I does not speak Korean. So there was a lot of body language communication.
3) to our horror, there wasn't any Eng gps available so we have to make do with Korean GPS. Gotten the staff to demo to us how to input phone number into GPS. It was pretty easy actually. Thank goodness we've grabbed a copy of Eng tourist map with the phone numbers of all the attractions and major supermarkets at the airport which we've relied very heavily on that.
4) for the next four days, I've became my driver friend's human GPS. I have to give instructions to my friend by reading from the GPS. The experience is fairly smooth except once where our hotel phone number was outdated. We've gotten a local to help us input the hotel addr into the GPS.
5) it's okay if there are some dents in the car as the roads are very narrow in city residential area because of cars parking at road side. We've bump into some other cars while navigating our way in the city area.
6) have paid ard $200 in total for the smallest car coz only 2 of us. We've only top up patrol once before returning the car in full tank.