It's easier for me to give up control and accept whatever the ride can dish out.
1) If you are afraid of heights, start will smaller, steel coasters. Most are smoother than the "woodies" (Tho, older steel coasters can have very jarring moments due to settling tracks and lack of maintenance - look for rust!!) Also, for the higher coasters (above 150'), suspended coasters are the way to go, as the track above your head gives the sensation of being "cradled." I have never felt anxiety on any of this type of ride.
2) NEVER ride a coaster if you are "pressured" to do so. Talk to the one that is pressuring you, and try to understand/overcome your fears. Your friend may know what you don't like about excitement, and the ride may be more tame than it appears. A solid discussion will alleviate most anxieties.
3) BREATH! ... Going up the lift hill can be very frustrating. If you have the feeling you are about to go into shock, breath deeply and swallow hard. Believe me, the ride down is far less troublesome than the ride up! Look around at your surroundings; try to see if you can see your house or hotel!! (If you are ridiculously afraid of heights, don't get on a coaster more than 200 feet on a two-seater ... i.e. Superman, Titan, etc ... Try your first mega-coaster with a four-seat spread, and sit in one of the middle two).
4) Once you get over your anxiety (after the third or fourth ride), DO NOT GET COCKY!!! Obey all the rules established! A rollercoaster is NOT a skateboard, or stunt bike, where you need to "up the fright factor" ... If you've become "comfortable" with a ride, seek out a more thrilling sensation on a BIGGER attraction. I've done everything including: standing up; riding backwards; and, once, I even climbed out of shoulder harness and sat on the restraint and rode the coaster with my arms flapping like a bird! (I was kicked out of the park ... obviously).
5) As Robert pointed out: coaster riding is the safest form of transportation on the planet!! Don't feel silly if you have to start with a "kiddie coaster." Some, like the Scooby-Doo, can be fun if you are on it with friends, and you joke around afterwards how silly it all was before you all went on!!
If it is your first time on a roller coaster, your natural instinct is pull forward, no idea why, but I saw everyone of our children do it on their first big coaster. Then complain that it made their head hurt. What I realized is that I had learned to make sure my head was back against the headrest of the coaster. So when we go to parks and we have friends with us that haven't been, I always tell them just before we go down or get launched to get their heads back. I even had one adult thank me when he got off the ride that was sitting in front of me who mentioned he never thought of that.
By having the head back, it prevents your head from rattling nearly as much, especially if you are in a coaster with shoulder harnesses.
Next is, if it is your first coaster, don't choose a wooden one, especially if you are a girl. You will be so sore. The only exception I have found is the Cyclone at Six Flags over Georgia.
We love Towers of Terror at Hollywood Studios as each ride has been different.
Mentally, I just totally relax. I try to feel like the biggest pile of mush I can. When I do that it is a great ride and my body just absorbs the ups/downs. Now, there have been a few times I have tensed up and really regretted it. I felt like I was a cartoon character that kept getting squished. "Light as a feather" just relax. I can't stress that enough.
Oh, lastly, empty your pockets before you get on. Our family has been hit by change, packets of gum and even a camera.