Since the release of in-car software version 9, Tesla Model 3 owners can program their own Key Cards and Phones without making a service appointment.
Note: Some Service Centers will still tell you that it is necessary to schedule an appointment to add/remove key cards to the system. That is not true.
All you need to do is tap General -> Locks.
A list of the programmed keys will display with the option to name, remove, and add additional keys (either phones or cards).
A currently authorized card is required to make any modifications to the keys, which is great because it prevents you from accidentally deleting all the programmed keys.
This process applies to Key Cards (which can be purchased from your Service Center), Model 3 Fobs (which can be purchased online), and virtual keys in the Tesla App.