Avoid punishment by following the rules. If it is to late for this approach, decide to take your punishment maturely and acknowledge it is a just result of bad behavior. If this level of maturity is beyond your ability, there are always alternate methods to evade punishment.
Promise your parents you will never misbehave again. Acknowledge you were wrong and have learned the evil of your ways. Point out that punishment is unnecessary because you have learned your lesson and will not behave badly in the future.
Convince them with actions not words and help out around the house. Clean your bedroom, do the dishes and feed the dog. Be the perfect, cheerful child your parents always dreamed of. Show your parents you changed your ways and the need to punish you for past infractions is no longer necessary.
Hope your parents forget you misbehaved. Ask to go out and neglect to mention any punishment issues. If your parents let you go out, never mention the topic of your forgotten punishment again.
Volunteer for a worthy cause during the time you are grounded. Most parents will allow you to attend the volunteer activities. Enjoy your volunteer activity. At least it got you out of your house.
Form an alliance with the parent who is not angry with you. Convince your "nice" parent to change your other parents' mind concerning your punishment. Hide if your parents realize your plan and decide to form a united parental front.