Replacing a battery on a Timex Expedition watch can be rather difficult, especially since you want to be able to preserve the watch's watertight qualities. While most people choose to take the watch to a jeweller to have this done, it is possible to do it yourself.
Make sure the little arrow on the back is aimed to the right. Then, insert a small flat head screwdriver into the notch on the edge, and lever the back open. Place the back to one side.
Unscrew the clip holding the battery (if your model has a clip), and remove the battery.
Use plastic tweezers to put in a new battery. Do not directly touch the new battery. Screw the clip (if it has one) back on.
Replace the gasket that seals the watch. Then lightly coat the gasket with a silicone-based grease.
Align the back with the little arrow aimed to the right again, then carefully press the watch between two pieces of wood that are being held by a small vice, until the back seats itself.