The Player Garage begins life as a concrete platform outside the player's home.
It can be constructed by reaching Friendship level 25 with your brother, Francis. He will build it in exchange for bringing him 48 pieces of firewood, after starting his quest. The firewood must be delivered in a special loading zone that will appear near his truck; not the loading zone at the end of his driveway. It will take 6 in-game days for him to complete it.