Turn off the Craftsman 12 HP mower. Pop open the front hood over the Briggs & Stratton engine.
Locate the mower's flywheel. This completely circular assembly will be immediately visible at the top of the engine block. The flywheel has an iron cover. Remove the bolts in this cover using your socket wrench and pry the cover off.
Place your flywheel pulley over the exposed Craftsman flywheel so that the pulley's arms can be lowered down directly against the flywheel's exposed outer shell. Tighten the bolt on the center of the pulley with your wrench until the resulting pressure causes the flywheel to come free from the engine block. You can see the top of the blade's clutch shaft now that the flywheel has been removed.
Find the Craftsman's oil pan. This square pan will be directly below the removed flywheel at the underside of the engine block. Remove its bolts with your socket wrench and pull the pan away to reveal the bottom of the shaft. This will allow you access to the shaft.
Remove the visible bolts along the revealed clutch shaft using your socket wrench.
Strike the top center of the clutch shaft with a rubber mallet, directly where the center of the flywheel formerly resided. This will dislodge the shaft and allow for replacement.
Push the new shaft into place.
Follow your disassembly procedure in reverse to rebuild the oil pan and flywheel around the blade shaft.