How soon after giving birth can you get pregnant again?

Ovulating. As soon as you resume ovulating, so in theory the first month after giving birth. In practice that's pretty rare, and probably isn't such a great idea.
Any time. I tell patients that there are no guarantees and I have seen people get pregnant again in 4-6 weeks, but I personally tell them they should give time for the body to rest and allow a little gap between children. My own kids are 3 years apart and seemed like a perfect spread for us.