Open the back of a wrist watch using either a sharp-edged tool, a friction tool or a screwdriver, depending on the type of watch back you have. Screw-down watches require a friction tool, screw-back watches require a screwdriver, and snap-off watch backs require a sharp-edged tool.
Several different types of friction tools exist for removing screw-down watch backs. These include expensive jeweler's wrenches all the way down to simple soft rubber balls. To use a soft rubber ball, hold the watch in the palm of your hand with the back facing up. Press the ball firmly against the watch back while turning it counter-clockwise. Once the back becomes loose, finish unscrewing it using your fingers.
For a watch with a snap-off back, use some kind of sharp-edged tool to pop off the back. Specialized jeweler's tools exist for popping off watch backs, but you can also use a small flat-head screwdriver. Simply wedge the thinnest edge of the tool between the edge of the back of the watch and the case, and push upwards. Use caution, as the sharp edge can easily damage the finish on the watch, and it can potentially cause personal injury.
Most screw-on watch backs can be removed with the kind of small screwdriver available in eyeglass repair kits. Some watches use exotic screws that require tools available from a jeweler or specialty store.