Technically a brazillian wax involves the complete removal of hair from the buttocks and adjacent to the anus, perineum and vulva (labia majora and mons pubis). Basically, everything from the top of the "lips" down to the butt. Most people will opt for a landing strip in the area above the "lips" or a triangle or nothing at all. Some waxers will do designs.
There are different types of wax that salons may use. Some use the regular "yellow colored wax" that is used in combination with a cloth to remove the hair. Some use this "blue wax" that applies on very warm and thick, cools on your body, and the wax is removed without the use of a cloth. I think the yellow wax does a better job, but that's just me.
The waxing can be very expensive. Around where I am, it can cost anywhere from $30-80 a pop depending on the salon and how much hair you have. I usually get it done once every 8 weeks.
Good waxers will chat and talk to you to make you feel less self conscience, especially if it's your first time. You will have to get into various positions so that the waxer can have you in the best position to wax and remove hair. Some are quite amusing to me. I guess I got over my initial shyness.
Personally, I hate shaving because as the hair grows back, it itches like hell. With a clipper, I'm deathly afraid a piece of hair will snag on the blade. Besides, I just can't bend over fall enough to see what I'm doing.

I did a brazillian a few years ago and have been doing it ever since.
Hubby once asked me if I'm "used to it now" since I've had it waxed for a while now. My response is... no. It still hurts like hell. But I do like the 'cleaness' of how it feels without the hair, especially during that time of the month. The pain is still there at every session, but it does get easier though. My first session was 45 mins long. Now my waxer can get me in and out the door in about 20 mins. It still stings at the initial ripping, but not as bad.