Take the voucher(s) to the windows next to the entrance of Disney Quest. They require ID to match the resort reservation name. You will then receive an RFID enabled ticket (looks like a credit card) in exchange for each voucher which you can use to obtain entrance to Disney Quest at the main entrance. (See photo - ticket windows to the side of the main entrance, the main entrance is under the Disney Quest lettering)
For mini golf vouchers, you just give the cast member your voucher instead of paying at the cash register. No fancy exchange required.