Changing the belt on a tumble dryer is something most people with moderate mechanical ability can do at home without the help of a professional. If the dryer sounds like it is running normally but--when you open the door--you can tell the drum is not turning, then it is likely a broken belt problem.
Never work on a dryer without fully disconnecting the unit from the electricity or gas.
Typically, it is easiest to replace a broker clothes dryer belt from the front. Move the unit out so you have space to work. Remove the lint screen and any screws that may be holding the front and top in place. Use a flat edge such as a screwdriver or putty knife to release the clips holding the top panel, then the front panel, in place. Be careful not to scratch the finish. The top panel may be attached to wiring, so just tilt up or flip back to rest on the back of a chair or have someone support it while you work. There is no reason to remove all the wiring. Take the foot panel off and support the drum with something solid, such as wood blocks to hold it in position. Set the front panel to one side.
Slip off the old belt. Most shops that off dryer repairs also sell dryer replacement parts. Either take the belt with you or make some phone calls to locate a replacement belt. Make sure to carry the tumble dryer model information with you.
Slide the replacement belt into position. Use grooves or marks on the drum from the previous belt as a guide for proper replacement. You will need to lift the drum off the support slightly to put on the new belt.
The belt fits around a pulley that is attached to the motor. You may need to loosen the pulley to fit the new belt around it before tightening it. Roll the drum a few times to make sure the belt is following the same path as the original belt. Reassemble the dryer.
While you have the dryer open, this is the perfect time to clean out accumulated dust and lint. Wipe with a clean cloth or use a hand vacuum for the task.