Drive the riding mower onto a flat surface, such as a garage floor. Put the lawn tractor in "Park" and set the parking brake. Remove the key from the ignition. For added safety, remove the wire from the spark plug.
Set blocks of scrap lumber on either side of the edge of the mower deck. Lower the mower deck onto the blocks to reduce tension on the deck's lift linkages.
Remove the locking pins and washers that hold the deck linkages to the mower's body. Each model is slightly different, so check your owner's manual for the locations. There are usually two linkages on both sides of the back of the mower and two on both sides of the front. Set the locking pins and washers in a safe place so you don't lose them.
Unwrap the mower's belt from the engine's idler sheave, if the belt is still intact. Remove the wooden blocks. Pull the mower deck out from under the body of the riding mower. Loosen the belt tension pulley.
Thread the new mower belt around the pulleys and idler sheaves. Perform any other maintenance to the deck, such as sharpening the lawnmower blades, at this time.
Slide the mower deck back underneath the mower. Put the blocks under it. Connect the linkages again and replace the washers and pins. Slide the belt around the engine drive sheave. Check that the belt remains in place as you tighten the belt tension pulley.
Remove the blocks from under the mower deck. Raise the deck. Start the lawn mower and take it outside. Mow some grass to ensure the belt is working properly. If it appears to be slipping, tighten sheaves as necessary, following the directions for your specific model.