Teams
A team consists of seven players:
3 Chasers
2 Beaters
1 Seeker
1 Keeper

The Field
Prime seats would be between the two goals at about the level of the goals.  There are three goal hoops, fifty feet high, at each end of the stadium.  IV-96  There is no apparant limitation as to how high the players can go.
 

Equipment

Brooms
Quaffle - Scarlet, about the size of a soccor ball, this ball is used to score
Bludgers - Black heavy balls slightly smaller than the Quaffle, they can injure a player who gets in the way.  The Beaters keep them off the other players and try to direct them at the opposing team.
Golden Snitch - This small, winged, gold ball is the size of a walnet, is elusive and hard to spot.  The Seeker capturing it earns his team 150 points and it ends the game.  Usually the team capturing the Snitch will win the game, but not always.

Officials
One Referee on broom with whistle.  He enforces the rules and assigns penalties.
 

Rules:

The game begins by the Referee releasing the four balls and blowing his whistle.  A team scores ten points for succesfully getting the Quaffle through one of the goal rings.  The game ends once the Golden Snitch has been caught.  The longest game on record is one of abouut three months.  I-169

Substitutions of players is allowed, though seldom done unless the game drags more than a few hours.

Penalties -
There are 700 ways of committing a Foul in Quidditch.  All 700 occured in the World Cup match of 1473.  I-181  Most of them are no longer possible given the ban on the use of wands by players and the audience.

Those we have seen specifically called are:
Cobbing - Excessive Use of Elbows - Penalty Shot - IIV-109
Delibrately trying to run into an opponent - IV-111
Penalties can be awarded due to audience or mascot misconduct.

Standard Strategies:

Hawkskead Attacking Formation IV-106
Porskoff Ploy IV-106
Wronski Defensive Feint - Dangerous Seeker Diversion (IV-109)

Quidditch is played on three levels.  The intermural level of school competition between houses, the professional level, run similarly to the soccer leagues in England, and the international level of the Quidditch World Cup.

International Teams We are aware of
Bulgaria - Runners up in 1994
England - Lost to Transylvania
Ireland - Winner of the 1994 Quidditch World Cup
Luxemburg - Beat Scotland
Peru - Lost to Ireland
Scotland - Lost to Luxemburg
Transylvania - Beat England
Turkey
Uganda - Beat Wales
Wales - Lost to Uganda

Professional Teams - There are 13 Professional Teams in Great Britain
The full list can be found in Quidditch Through the Ages, the following are mentioned in the books:
Chudley Cannons - Logo of two Cs and a Cannonball, Orange Robes
Puddlemere United - IV-84
Wimbourne Wasps - IV-86 -IV 524 - Logo of a Wasp - Yellow and Black Striped Robes.