Fossil watches are usually pressure sealed to keep moisture out and extend the life of the watch. They offer a battery replacement service if it goes dead, and this is certainly a safe option if you just need to replace the battery. With a warranty, it only costs £11 including shipping. If you are set on removing the back of the watch yourself, then it is fairly easy---just be careful not to get anything on the inside.
Take the watch to a clean room with as little dust as possible, and place the watch inside a large plastic bag (this will help minimise particles that can get into your watch).
Take a flat, dull knife, fine-point tweezers or a thin, flathead screwdriver and insert it into the separation line between the back plate and the casing.
Gently twist the blade as you rotate around the casing. As the pressure loosens, you will hear a pop.
Remove the back and set aside.