Technically speaking, self-driving cars would not park, what they would do is “standing”. Whenever they are not serving anyone, they need to find a place to wait. The cars would have maps of all parking spots and parking rules, and the ability to see if spots are vacant or occupied.
Nowadays, already many parking lots are moving to support parking reserved and purchased through the internet. Most of the time, self-driving cars can get a discount because they can park somewhere far from the gate.
The self-driving car can also double park or even triple park on streets if possible. When it is high traffic, they can drive themselves around automatically. They will drive till there is an empty spot found. They can drive off to pick up for the next person who needs a lift. They can re-direct themselves to charging stations as well.