Auto-Park
You can only have one owned vehicle out at a given time[1]. If you wish to spawn another owned vehicle, you will need to park your vehicle first. There are four methods of parking.
In order to park your vehicle, you will either need to be in or right next to the vehicle. In case your vehicle is far away, try to locate it with the map legend. Look for the 'Personal Vehicle' blip and place a waypoint.
B ► Auto-Park
By holding the B button (keyboard), a radial menu will show up. In that menu, click on Auto-Park. Confirm by pressing F5 and your owned vehicle will despawn.
M ► Car / Options ► Autopark (Delete)
Navigate via the M menu, M ► Car / Options ► Autopark (Delete). Confirm by pressing F5 and your owned vehicle will despawn.
M ► Zdelete
Navigate via the M menu, M ► Zdelete [2]
This option only shows up if you are not inside a vehicle.
For big vehicles, such as airplanes, you'll have to run around (and under) the vehicle and spam Zdelete until the vehicle despawns. This option is useful for cleaning up abandoned vehicles, as you can Zdelete other players' and NPC vehicles.
Parking inside a Garage Marker
Move your vehicle inside of a garage marker and look at the context menu in the bottom right. This will show what key combination you need to press in order to park the vehicle. By default, on keyboard, this is (hold) Spacebar + press C