Generally speaking, a dead tarantula will be upright with its legs curled underneath, so if you find your tarantula laying on its back, there's a good chance she is just starting to molt.
Molting usually takes up to a few hours, so this is a time to keep an eye on your tarantula, but never touch it! Your tarantula is extremely fragile and vulnerable at this time, so should never be touched until well after the molt has been completed (a week is a good start).
Also make sure there are no crickets in with the tarantula over the same time period. There are other signs that will precede a molt, as well, such as changes in appetite and activity among others.
While you shouldn't touch a molting tarantula, it doesn't hurt to watch from a respectful distance. A molting tarantula is rather a wondrous sight, as they split their outgrown exoskeleton and peel themselves out of it.
Have a look a this YouTube Video of a molting tarantula, aptly titled "and Her Skin Fell Off." It is a very condensed time lapse that shows a beautiful tarantula clearly pulling itself out of the molted exoskeleton.
Image © horehoundpie