One of the most endearing features of ultimate is that its core rules are very simple: Pass the disc between your teammates until you catch it in the end zone for a score. Do not walk or run with the disc when you have it. If the disc is caught by an opponent, touches the ground, or goes out of bounds, the other team gains possession. Everything else is simply details!
USA Ultimate Rules
Most players play by the latest set of USA Ultimate rules, currently the 11th Edition. If you intend to play ultimate competitively, you should read the whole rulebook. Most of us will get by with just the basics, so here is a more concise version to get you started. (source: USA Ultimate)
Ten Simple Rules:
The Field: A rectangular shape with end zones at each end. A regulation field is 70 yards by 40 yards, with end zones 25 yards deep.
Initiate Play: Each point begins with both teams lining up on the front of their respective end zone line. The defense throws ("pulls") the disc to the offense. A regulation game has seven players per team.
Scoring: Each time the offense completes a pass in the defense's end zone, the offense scores a point. Play is initiated after each score.
Movement of the Disc: The disc may be advanced in any direction by completing a pass to a teammate. Players may not run with the disc. The person with the disc ("thrower") has ten seconds to throw the disc. The defender guarding the thrower ("marker") counts out the stall count.
Change of Possession: When a pass is not completed (e.g. out of bounds, drop, block, interception), the defense immediately takes possession of the disc and becomes the offense.
Substitutions: Players not in the game may replace players in the game after a score and during an injury timeout.
Non-contact: No physical contact is allowed between players. Picks and screens are also prohibited. A foul occurs when contact is made.
Fouls: When a player initiates contact on another player a foul occurs. When a foul disrupts possession, the play resumes as if the possession was retained. If the player committing the foul disagrees with the foul call, the play is redone.
Self-Officiating: Players are responsible for their own foul and line calls. Players resolve their own disputes.
Spirit of the Game: Ultimate stresses sportsmanship and fair play. Competitive play is encouraged, but never at the expense of respect between players, adherence to the rules, and the basic joy of play.
Fun rules additions:
Money Disc - Bring out a special disc, usually a neon orange one. When that disc is in play, the point is worth 2 points instead of one to the team that scores it. Both teams are allowed to choose one point during the game that will be a money point. They must do so before the pull by throwing the money disc out to the players on the line. It usually makes the most sense to choose a point when your team will be receiving the pull.