Me! I was always terrified of roller coasters before Disney World, even little kiddie coasters, but decided to ride for my kids. Turns out I love them! Everyone is different, but this is what worked for me: ahead of time, I did a little research to reassure myself that the rides are safe. Disney has an excellent safety record, which I find very reassuring. Most of the roller coasters are relatively slow and not super high. Watching ride videos might help, too, so you know what to expect.
I started with the rides I found least scary and worked up from there. For me, the scariest part is going up a high lift hill. I also do not like rides that are too rough and make me like the ride is about to break. I know a lot of people say to start with Barnstormer because it is little and over quickly, but that is actually my least favorite ride, as it has a scary (for me) lift hill and a very rough ride. I do not plan to ever ride it again.
While it certainly would not work for someone mostly scared of big drops, I actually was the least nervous about Splash Mountain. None of the lift hills are particularly high, and the big drop is somehow less scary for me because it ends in water. Silly, but there you are. It definitely made me nervous the first time, but now it is one of my favorite rides!
Both BTMRR and Seven Dwarfs are good for someone like me because there are no big lift hills, and even the drops are fairly short. Seven Dwarfs is smooth as silk, which alleviates a lot of my fears. BTMRR is a little rougher, but not bad by any means. These are also favorites.
I was not sure I would be able to ride Everest or Slinky Dog Dash until I felt comfortable on the others, Everest because of the big lift hill and Slinky because it looks so much like the typical roller coasters that scare me. Once I was comfortable on the others, however, I gave them a try and found them to be super fun, too! I am glad I did not start with them, but that is just me. Others may be more nervous about different elements than me, making those rides an easier fit for them. Space Mountain is another that I put off, and I am glad I did -- it is very fun, but definitely a rough ride. Tower of Terror still scares me, but not enough to avoid it.
Long story short, my advice is to figure out what you are scared of and ride the rides with less of those scary elements first, then build up. Have fun!