Turn the table saw off and pull the plug from the wall outlet. Push the blade guard back to expose the table saw blade. There is a metal plate that lies beneath the blade and is secured to the table saw frame with a set of screws (the exact number depends on the model and make of the table saw). Unscrew the retaining screws and pry the plate up by hand from the saw blade well.
Raise the saw blade by pushing the bevel lever to the up position (it should be marked on your table saw). Take two wrenches and place the open ends on either side of the blade--one on the axle and one on the end nut; the size of the wrench depends on the make and model of table saw. Rotate the end nut off while holding the axle stationary. Carefully remove the saw blade once the nut is removed. The blade should always be treated as sharp, no matter how dull it looks; use work gloves to be safe.
Go beneath the table saw and locate the saw motor to the side of the blade well. Unplug the power cord from the rear of the motor. The motor should be secured with four bolts, one on each corner flange of the motor housing. Unbolt the retaining bolts with a wrench, being careful to support the weight of the motor so it does not fall. Once the bolts are removed, carefully pull the motor out.
Slide a new motor (same voltage and horsepower) into the table saw and match the flange holes up to the bolt holes in the frame. Thread all the retaining bolts in by hand first. Then tighten the bolts in with a wrench. Plug the motor power cord in and replace the blade in the table saw. Plug the table saw back in and turn the saw on to verify that the motor works.