GCD, not all babies even need burping. Usually, as Lulu said, mums try to burp when the baby pulls off and before changing sides. There is no hard and fast rule though, and if no wind comes up, don't worry. The vomitting is very normal also and nothing to worry about.

Just one other thing (sorry to overload you with so much information), it is best to feed from one side until the baby is finished, and then offer the second side (that is, don't "time" the feed on the first breast and move him to the other side because the time is up). In the early days babies don't often take the second side during a feed, but usually mums offer it anyway. One day when he is bigger he will probably start wanting it. And if he wants it now, that's ok too!