Most male buns do very well after a neuter. Some might want a heating pad/hand warmers/ hot water bottle wrapped in a blanket to snuggle up to. My Bam did, but he was older when he was neutered. Serve water in a bowl instead of a bottle, because a newly anesthetized bun might not feel up to bothering with a bottle. The most important thing is to get him to eat something. Fresh herbs are often appreciated, for example cilantro, parlsey, dill or mint. Pellets is often the last food type they return to.
Make sure the vet gives him a painkiller for you to distribute at home, if needed. Metacam is well tolerated by bunnies. Painkillers makes it less likely that the bun will try and chew at his incision site. The outer wound is often glued shut, so there are no stitches. As Mikey says, if you see him go for the wound, a cone is necessary and if he manages to rip sth open, a vet visit asap is required. Check wound every day as the others have said already.
Most neutered boys need to be confined for 2-3 days only, but some can have a bit of playtime on days two and tree. No jumping and climbing the first week.