At most of the airports you will have the possibility to choose for valet parking. When choosing for valet parking u will hand over your car at the airport, and you don't have to drive to the parking first.
On the day of departure you will drive to the airport. Most of the times you will have to contact the parking before arrival. They will make sure that a driver is waiting for you at the airport to be at your service. They will check your car for damages before you hand over your car keys. The driver will park your car at the parking, and you can check in for your flight.
On the day of arrival you will need to contact the parking after receiving your bagage. They will make sure that your car will be waiting for you at the airport. You will receive your keys back after an inspection of your car, and you can continue on your journey home.