Alex R, what goes on in a pointe class depends on the level of the class. Typically, a beginning pointe "class" is actually just the last 10-15 minutes of a regular ballet class. The students put on their pointe shoes (see the link in the post above - thanks, IWantCaNdy3o3!) and do their first exercises facing the barre with both hands resting on the barre. They practice rising to the full pointe position on both feet, without letting their knees bend. They learn to do this both slowly, going through the half-pointe position (standing on the balls of the feet) and quickly, in one snapping movement. They learn how to "spring up" on pointe from a demi-plié (standing with the knee(s) bent and the heel(s) on the ground). They practice balancing sur les pointes on both feet. They also practice certain exercises in pointe shoes that don't involve actually standing on their toes, for example learning how to point their feet wearing these specialized shoes.
Gradually, as strength is built up, the students rise/balance on one foot. At some point, the simpler exercises are performed in the center of the room, without the barre.
Eventually the students are strong enough to handle a much longer pointe class, separate from their regular technique class. Over the years, the exercises get more and more difficult, until finally the advanced students are performing combinations of steps that actually come from well-known classic ballets, or are at least their equivalent in difficulty. They often learn complete solos from ballets.
It's kind of hard to describe steps to someone who is not familiar with the terminology, but I hope this gives you some idea of what it takes.
<small>[ 15 July 2004, 12:03 AM: Message edited by: djb ]</small>