It's hard to say exactly what happens to Bod after he leaves the graveyard for the last time in The Graveyard Book. Though he has left the graveyard several times before, to go to school, to investigate his childhood home, and to see the ghosts dance the Macabray, for example, the last chapter of the novel implies that this will be his very last time leaving the graveyard and that he won't be coming back.
Though Neil Gaiman doesn't explicitly tell us what Bod does when he leaves, we can make some educated guesses based on what we are given. First, he's given a wallet full of money, a passport with a new identity, and a suitcase full of belongings. These things are all new to him; he hasn't needed them in the graveyard, and this is just the beginning of preparing for life as a normal human being rather than a human surrounded by ghosts.
Until this point, Bod's life has been rather sheltered. While he gets into all kinds of adventures, he doesn't get to see much of the real world. His life in the graveyard is interesting to us because we don't live that way, but, from Bod's perspective, things we find commonplace are interesting. He tells Silas that he wants to leave footprints in a desert and play football, and that he wants everything; in essence, the life he has not been able to experience because of the threat of Jack.
His last encounter before he leaves is with Mistress Owens, his adopted mother. She sings a familiar song to him, advising him to:
"Kiss a lover
Dance a measure,
Find your name
and buried treasure...
Face your life
Its pain, it's pleasure,
Leave no path untaken."
Unfortunately, the book ends as Bod leaves--we don't get to see what he does. But his own optimism, his hopes, and Mistress Owens' song give us a strong hint that what he'll do when he leaves is experience life and all it has to offer, whether that matches exactly what Mistress Owens suggests or whether it looks quite different. When he leaves the graveyard, Bod aims to do everything he couldn't do there--meet people, travel, see everything the world has to offer. He's embarking on a new adventure in his life, and while we don't see it happen, we know that almost everything he experiences will be new to him.