I felt the same as you, I was worried i'd move, my eyes would move etc. I'm also incredibly sensitive with anything near my eyes to the point of never being able to use contact lenses as I couldn't put them in, the optician wouldn't let me leave until I could prove I could put them in and take them out. Every time I tried my eye would naturally shut and I just couldn't do it.
During the procedure you can't move, you're led down and your head is basically clamped down. The technology is advanced enough that if your eye moves during the surgery that it can track it. Feeling wise, the most uncomfortable part of the procedure is when they're putting the eyelid clamps in. I won't lie that's not very pleasant but nothing too bad. They will put numbing drops in so you don't actually feel anything through the eyes.
The procedure for Lasik is (I might be a bit sketchy here, I had it done over a year ago);
1. Lie down
2. Drops go in
3. Eyelid clamps go in
4. They move you under the first machine which cuts the flap. The machine has a suction pad on it that feels like pressure against your eye to try and keep it in place. No pain, but definitely feels a bit weird. The closest thing I can think of is if you pressed swimming goggles against your eyes.
5. The surgeon then moves the flap back, this looks weird as you can see your eye losing focus
6. They move you under the second machine and it does it's reshaping job. You feel nothing.
7. The surgeon puts the flap back in place and takes the clamps off
That's it job done, the whole process took about 5-10 minutes.