Slam competitions distinguish themselves from other poetry contests by giving equal weight to both writing and performing. In other words, they reward poets not only for what they say but also how they say it. Sometimes slight variations on the official rules are allowed, but here's how a slam typically works.
Whoever is hosting the slam selects five random judges from the audience. These judges are instructed to give scores from one to 10 to each poet on stage based on the quality of both the poem and the performance. Most slams are open to anyone who signs up. Usually, the poet must have written the poem she or he performs.
Each performer typically gets three minutes to read the poem. When poets go over the time limit, they get points deducted from their scores. No props, costumes or musical instruments are allowed.
Of the five resulting scores for each poet, the scorekeeper drops the highest and lowest, giving the performer a maximum score of 30. Poets with sufficiently high scores are admitted to a second round. In this manner, a champion is eventually determined.
Poetry readings have an unfair reputation of being boring. Slams have gone a long way in changing this. They're designed to increase the entertainment value of live poetry events. As such, they're not for the faint of heart. At the end of, or even during, a performance, audiences are usually allowed to boo, hiss, howl, cheer or do almost anything else short of inflicting bodily violence. At Chicago's Green Mill, where the poetry slam first took off, audiences who really hate a poet are actually allowed to signal that the poet must leave the stage, even if they aren't finished with their poem. Harsh! Although not every slam allows this level of cruelty, audiences are generally encouraged to express themselves however they see fit.
An anthology called Poetry Slam: The Competitive Art of Performance Poetry is considered the definitive guide to slam. It's chock full of useful essays and samples of successful slam poems. If you're interested in learning more about the culture surrounding slams, this is an excellent place to start.