If you choose to use the Valet parking service at the Deluxe resorts, you will be charged $6 per day, which can be added to your room charges. You do not need to use valet if you do not want to.
If you are not staying at a Disney resort, I don't know if there is a way to buy a weeklong parking pass; You pay for parking as you enter the lots, and if noone here can give you more information, I'm sure the CM at the parking gate can help you!
Have a great trip!