Why Should We Think Luke and Acts Have the Same Author?

The Gospel of Luke and the Acts of the Apostles are widely understood to be a two-volume set, written by a single author.

Given that we've spoken before on Misquoting Jesus about how difficult it is to identify authors of ancient texts, why are scholars so sure that these two texts share the same author?

Who was that author, and why write two books when they could have written one?!