Twas an interesting experience, and not necessarily for the faint of heart.
I believe that since I had it done, there have probably been advances in techniques, but I'll describe the state of the art as it was around 6 years ago.
Back in the day, there were two options, and I forget what one of them was called. The first option was to have the surface of your eyes "carved" with a laser. This was done one eye at a time, with a gap of days between eyes. I understand the recovery for this was moderately painful, and I think it was the first technique offered.
The second option, LASIK, was known as the "flap & zap". This is what I had. It does both eyes in the same appointment, and your recovery time is effectively overnight.
First you need to have an appointment or two to measure your eyes curvature and to work out the desired changes. The worse your eyesight is, the more chance that you will not end up with 20/20 vision. The technique was better for short sighted folks than long sighted folks, and it can also correct astigmatism (rugby ball shaped eyes).
So, onto the procedure. First up, you sit on a bench and the optician/surgeon marks your eye with a permanent (ish) marker so that he knows which way is up when you are lying down. This is important as when you do lie down, your eyeball will rotate a bit. Then you lie down. You then get some eyedrops that are a local anaesthetic (I think you have some pain receptors there!). Next up, they tape back your eyelids on one eye and get out a whizzy little gadget called a "micro-keratome" (I think) which is effectively a miniature circular saw that runs along a "U" shaped rail. It also comes with a sucker, which they attach to your eyeball prior to flicking the switch to power it up. Here, at the time, surgeries were offering either the "U" shaped rail, or some surgeries offered the "C" shaped rail. The "C" shaped one was the "old-tech", and there were issues with the flaps then not reseating themselves properly as the hinge part in the open end of the C would be somewhat strained.
Anyhow, they switch on the saw and carve a "U" shape out of the surface of the eyeball. Here your vision goes a tad blurry due to the tears (but no pain!). They remove the saw (leaving the sucker, I think, as it helps stabilise your eye position) and you see the surgeon appear wielding a pointy stick which he proceeds to poke you in the eye with. What he does is flip the flap up. Here your vision goes really blurry. Next, a ruddy great machine with a small red light on is pushed into place above your eye. This is the laser, and you stare into the light while you hear the high frequency zap-zap-zap (think the sparks from a piezoelectric lighter) and smell the burning flesh (not too unpleasant). I like to think that I could see where the laser was hitting as it carved my eye up - I think it swept around in an anti-clockwise direction. Anyhow, once the zapping stops your eye is carved into shape. It's worth noting that the laser equipment can tolerate some eye movement as it has a camera pointed at your eye too, to ensure that the zap it's going to do is aimed at the right place. It's also a gradual process so that it can afford to be slightly out a few times. Still - you need to make an effort to keep your eye from wandering.
Next up, you see that blurry shape that is the optician/surgeon come in with that pointy stick, and the flap is then flipped shut. The sucker removed, and an eye-patch applied. Then you repeat it on the next eye.
After it's all complete, you go sit in a dark room for an hour or two before you are allowed to go home. Wear sunglasses for the way home and for the rest of the day. You would also be sent home with some drops for your eyes (that anaesthetic, again) that you should put in every hour or so or suffer some discomfort. I stuck my drops in and then went straight to bed - slept like a baby (which is a misnomer, in itself) and woke up with slightly sore eyes, but near perfect vision.
Over the next week or two, expect fluctuations in your eyesight, but it should settle down.
Note: you have a small, but non-trivial chance of ending up with imperfect vision that may still require correction for things like driving.
Was it worth it? Yep, indeedy. I was rather fed up with glasses, and contact lenses were a right pain in the behind.