I like long walks on the beach and beating people up...
When you battle, 4 characters are randomly selected from your deck (which must contain a minimum of 8 cards) and will fight a total of 4 rounds versus your opponent's 4 characters. The winner of each round will reduce the loser's life total by the damage (5) listed on the winning card (adjusted by any abilities and/or bonus that is currently active).
The loser of the battle is the player with the lower life total at the end of the 4 rounds (or sooner if a life total is reduced to 0). You start with 12 life points and 12 pillz, although there are ways to increase or reduce that amount during rounds depending upon the abilities of your characters.
The winner of each round is determined by a relatively simple formula. Your card's Power (5) is multiplied by the number of Pillz (6) you have used in that round. The attack can also be modified by abilities and bonuses that are active in that round.
Power * 
Pillz = 
Attack
The Battle Screen
(1) Opponent Nickname
(2) Remaining Pillz and Life Points of your opponent
(3) Character played by your opponent
(4) Your Pillz and Life Points
(5) Power and Damage of your character (this one P:5+2 / D:3)
(6) Pillz you are using (here 4)
(7) Your character Attack (5+2 power * 4 Pillz = 28 attack)
Information here has been taken from the Urban Rivals website:
http://www.urban-rivals.com/game/rules.php?show=battle
