He doesn't in the story. Getting a piece of land to call his own is his dream, along with Lennie's and Candy's. They think the dream is in reach only to have it shattered by Lennie's accidental murder of Curley's Wife, and the subsequent death of Lennie.
Now if you're asking whether I think George ever gets his piece of land, Steinbeck gives us no clue on this. Most people who lived through the Depression did eventually recover their lives economically, but the impression we get in the story is that George is well and truly a broken man from his being forced to kill his best friend. I was left with the impression that he would never recover.