Open the front engine hood of your Craftsman lawn tractor and look at the battery. Disconnect the red "positive" and black battery cables from the battery using a socket wrench. This is for your own safety.
Locate the solenoid on the engine's frame between the battery and the starter. The red positive battery wire also connects to the solenoid. Turn the bolts counterclockwise with your socket wrench to remove the battery wire. Remove the wire on the opposite side of the solenoid in the same manner.
Remove the wire harness from the solenoid. This is made up of a number of smaller wires. Lift up on the retainer clip holding the wires in place using a knife, then pull the wires up and out.
Remove the four bolts holding the solenoid to the frame of the engine using your socket wrench. Pull out the solenoid.
Put the replacement solenoid into the machine where the old solenoid was located. Visit your local lawn care store or contact Craftsman to obtain the correct solenoid for your Craftsman mower model. Make sure you have your model number on hand when doing this.
Connect both the wires back onto the solenoid's bolts on either side of the part using your socket wrench.
Place the wiring harness back onto the solenoid and ensure it makes contact with the Craftsman solenoid's metal electrical connectors.
Reconnect the red positive and black negative battery cables to the Craftsman lawn tractor's battery. Shut the engine hood.