How do I watch downloaded movies?

From the Videos app

The movies have to be part of the iTunes library on the computer and can then be synced to the device, or, if you buy the movie using the iPad, it will be downloaded onto the device.

Movies you did not buy in the iTunes Store have to be converted into a supported format by using 3rd party software, then imported into iTunes on the computer and synced after that.

Also check these articles for more info:

Why can't I transfer videos to my iPod?

iPod plays video but not audio of some exported files

Frequently asked questions about viewing and syncing video with iTunes and iPod

iPod plays audio but not video of movies

Thanks James! It was driving me crazy why I couldn't watch a movie I bought and downloaded on my Ipad without being hooked up to wi-fi. You were a big help.