Set the alarm to go off and let it ring until it stops. This will release the power stored in the alarm mechanism. Do not do this if your clock is battery-powered.
Unscrew and remove the two handles in back by twisting counterclockwise. This should allow you to remove the plate covering the back of the clock.
Use the pliers to unscrew the knobs on top of the two bells and the two feet. This is likely unnecessary if you have a small battery-driven clock. For these clocks simply unscrew the back plate.
Gently pull the clock mechanism out of the casing, pull the hands off of the face and place the clock face down.
Find the metal plates that attach the face to the clock mechanism. These project from the back of the face and are folded into slots on the mechanical unit. Straighten them out with pliers so that you may remove the face.
Behind the face is a big gear. Pull this out, along with the two smaller gears behind it.
Look inside the mechanism and find the balance spring, which will be a round metal coil balanced above a large wheel. The balance spring is attached to the casing by a pin, so remove the pin.
Spin the wheel below the spring counterclockwise and watch as the end of the coil comes out of its slot. The spring is now unattached.
Locate the screw that attaches the wheel to the base; unscrew this to remove the balance wheel and spring.
Locate the bolts holding the two main pieces of the body together. Partially unscrew the nuts holding these.
Locate the pallet fork. This is a small triangular piece with one curved side. It is located nearby the balance wheel. You should be able to remove this after you have unscrewed the nuts. Successfully removed, this will release the power of the main spring.
Continue unscrewing the nuts until you can separate the two parts of the mechanism body. You should see the large springs for the alarm and the clock now loose. You have now disassembled all of the major parts of a travel alarm clock.