How were the earth's continents different at the beginning of the Mesozoic era from how they are now?
At the beginning of the Mesozoic Era, all of the continents of the Earth were pretty much jammed together into one giant "supercontinent." This supercontinent was called Pangaea. It was not the first supercontinent, but it was the last (that has existed so far). Pangaea started breaking up somewhere midway through this era.
Follow the link below for a pretty good map of what was where during that time.
The Mesozoic Era began roughly 250 million years before the present. It lasted until somewhere around 65 million years ago. During this time, the dinosaurs were the dominant form of life on the planet.