Basic Explanation

Offense/Attacking:

• Each team has 6 players.
• As you move around the field, your teammates will also move accordingly.
• You can choose between automatic or manual control. In automatic control, you need not worry about moving your player.
• Each player has a preset amount of HP which is consumed as he/she moves around the field.
• Players that do not have the control of the ball regenerates their HP over time.
• You also have a preset amount of PS as it determines the success of your pass. Your PS must be greater than the amount required to reach your teammate.
• ST also has a preset amount. As the ball approaches the goal, it will decrease. You must have at least 1 ST to shoot the ball and it must be higher than the goalie's CA to score a goal.
• Every person can learn special abilities that cost more HP.

Defense:

• If the defensive player has a CU equal to or greater than the passing player PS he will intercept the pass.

• The offensive player can use the Breakthrough move that will allow them to avoid a defense.

• At certain times you can copy the opponent's techniques and set them for use later.

Links:
A full description of Blitzball would take far too long. Here is a link to an in-depth Blitzball guide by a man with far more time than I.