The Once and Future King
Action Points provide a player with the means to alter d20 rolls in dramatic situations, reflecting the luck that can change crushing failure into heroic success. Your character has a limited number of action points, and you must use them wisely, since you don’t replenish them until your character attains a new level.
You can spend an action point to improve the result of an attack roll, a skill check, an ability check, a level check, or a saving throw. When you spend an action point, you add the result of a roll of a 1d6 to your d20 roll to help you meet or exceed the target number for the roll. You can declare that you are spending an action point after you have already rolled the d20, but you must do so before the DM reveals the result of your roll. You can’t use an action point on a skill or ability check when you are taking 10 or taking 20. You can only use an action point once per round. (Players must decide to spend action points to improve their attack rolls before they roll their damage.)
At 1st level, you have 5 action points. Each time you attain a new level, you gain a fresh supply of action points equal to 5 plus 1/2 your character level, rounded down. Any action points you didn’t use at your previous level are lost. If your character is 8th level or higher, you can roll more than one d6 when you spend an action point. If you do so, apply the highest result and disregard the other rolls.
Please note that there are two action-point related feats you can select as you level, too.
The “Action Boost” feat has no prerequisites, and allows you to roll a d8 instead of a d6 when spending an action point.
The “Action Surge” feat requires a BAB of +3, and allows you to spend 2 action points to take an extra move or standard action in your turn.