At this age he's likely to only be awake long enough to feed and have a nappy change and then back to bed. My dd was often only awake about 2hrs total during the day at this age (after her morning feed and before her final night feed) - during the day she'd wake for a feed, and fall straight back asleep for another 3hrs. Just follow his cues for now and when he's showing tired signs just put him into bed. As he gets a little older he'll be able to stay awake for longer. If he's falling asleep while feeding, I'd gently wake him up, make sure he's had a full feed, change his nappy and then watch for sleep cues.
HTH
