I'm not sure what happens if it's a cat, but with a dog the just snip the balls off as far as I know. If they let him home on the same day (my ex gfs dog was in over night), expect him to be slightly groggy and for him to sleep a lot for a day or two. Other than that it's more or less business as usual, but don't go for any rough play until the stitches are out.
As Lacey says, don't let him nibble or lick the stitches. If you need to check the stitches do it visually, and try not to let him know you're doing it, because if you get close they can snap at you. It's not an aggressive snap, but more a keep away snap.
Dogs who have been fixed also tend to be a lot less aggressive to other dogs, and also humans. This isn't to say if someone broke in or attacked you that they wouldn't protect you, they still have their usual protect the pack instinct, just that they'll usually be friendly to other dogs and people you introduce them to. Having said that, it's not true for all of them and I do think it's down to how the dog is raised.