We go by the 11th edition USAU rules for ultimate which can be found here: Rules of Ultimate

The USAU Ten Simple Rules for Ultimate are: 

1. 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.
   
2. 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.
   
3. 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.
   
4. 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.
   
5. Change of Possession: When a pass is not completed (e.g. out of bounds, drop, block, interception, stalled), the defense immediately takes possession of the disc and becomes the offense.
   
6. Substitutions: Players not in the game may replace players in the game after a score and during an injury timeout.
   
7. Non-contact: No physical contact is allowed between players. Picks and screens are also prohibited. A foul occurs when contact is made.
   
8. 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.
   
9. Self-Officiating: Players are responsible for their own foul and line calls. Players resolve their own disputes.
   
10. 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.

Ultimate is self-officiated, which means the players are responsible for making calls that a referee would make in another sport.
Common calls are (see the USAU rules for details):


Fouls: A foul can only be called by the fouled player. He or she must loudly call "foul" immediately after the foul occurs.  There are several kinds of fouls:

1. 1. Throwing Fouls: A throwing foul may be called when there is non-incidental contact between the thrower and marker. If a throwing foul is con
   2. Receiving Fouls: If a player contacts an opponent while the disc is in the air and thereby interferes with that opponent's attempt to make a play on the disc , that player has committed a receiving foul. Some amount of incidental contact before, during, or immediately after the attempt often is unavoidable and is not a foul.
      • The player that is accused of committing the foul may contest the foul by saying "contest," or admit fault by saying "no contest." If the call is uncontested, the fouled player gains possession at the spot on the playing field closest to the spot of the infraction. If the foul is contested, the disc reverts to the thrower. 
      • When an in-bounds player in possession of the disc whose first ground contact will be completely within the end zone loses possession of the disc due to an uncontested foul, or lands out of the end zone due to an uncontested force-out foul (see USAU rules), that player is awarded a goal.
      • The Principle of Verticality: All players have the right to enter the air space immediately above their torso to make a play on a thrown disc. If non-incidental contact occurs in the airspace immediately above a player before the outcome of the play is determined (e.g., beforepossession is gained or an incomplete pass is effected), it is a foul on the player entering the vertical space of the other player.

1. 1. Blocking Fouls: When the disc is in the air a player may not move in a manner solely to prevent an opponent from taking an unoccupied path to the disc and any resulting non-incidental contact is a foul on the blocking player which is treated like a receiving foul. A player may also not take a position that is unavoidable by a moving opponent when time, distance, and line of sight are considered. Non-incidental contact resulting from taking such a position is a foul on the blocking player.
   2. Strip: If a defensive player initiates contact with the disc after an offensive player has gained possession of the disc, and the offensive player loses possession as a result, it is a strip. A strip is a subset of fouls and is treated the same way.
   3. Reckless disregard for the safety of fellow players or other dangerously aggressive behavior (such as significantly colliding into a stationary opponent), regardless of whether or when the disc arrives or when contact occurs is considered dangerous play and is treated as a foul . This rule is not superseded by any other rule.

Pick: A pick occurs whenever an offensive player moves in a manner that causes a defender guarding an offensive player (to be "guarding" you must be within 10 feet of the offensive player) to be obstructed by another player. Obstruction may result from contact with, or the need to avoid, the obstructing player. A pick can only be called by the obstructed player and must be called immediately. Play stops when the THROWER in possession of the disc acknowledges the pick has been called. If a call is made when the disc is in the air or the thrower is in the act of throwing, or if the thrower fails to acknowledge the call and subsequently attempts a pass, play continues until the outcome of that pass is determined. If the pick affected the pass, the disc goes back to the thrower. If the pick did not affect the pass, it stays with the catcher. The obstructed player is allowed to catch up to the person he/she is guarding


Travel: The thrower must establish a pivot at the appropriate spot on the field and keep all or part of the pivot in contact with that spot until the throw is released. Failure to do so is a travel and results in a stoppage of play.