Set the chain saw on a workbench.
Remove the four hex screws holding the starter assembly to the side of the engine. Pull off the spark plug wire from the spark plug. This will expose the flywheel and a small black box with the spark plug wire connected to it. This box is the coil.
Pull the ground wire off the back of the coil. Remove the two hex screws holding down the coil. Slide off the coil.
Place the new coil in position and loosely hand-tighten the hex screws. Place a business card between the two prongs coming off the coil and the magnets from the flywheel. Let the magnets draw the coil into position, then tighten the coil screws with the hex screwdriver. Remove the business card.
Connect the black ground wire onto the new coil. Plug the spark plug wire onto the spark plug. Reinstall the four hex screws into the starter assembly.