Turn off the water at the supply stop. Turn the stop knob clockwise until it stops and the water quits flowing. Remove the supply tube from the bottom of the tank with the crescent wrench. Inspect the supply tube and replace if it is damaged.
Flush the toilet to drain the tank. Hold the lever down until most of the water has drained and then sponge the rest out. Carefully remove the jam nut from the ballcock and remove the ballcock and float assembly from the tank.
Remove the two tank mounting screws. These should be on either side of the flapper valve. Care should be taken when backing these off. Using too much force can break the ceramic parts and ruin the toilet. Use penetrating oil and allow it to soak in if the screws are stubborn. Pad the floor with towels to prevent damage and place the tank on the pad.
Pad a crescent wrench with a rag. Hold the flush mechanism with this wrench inside of the bowl. Remove the jam nut from the outside of the bowl with the channel lock pliers. Use caution and to prevent tank damage, do not force the nut. Use penetrating oil if it is stubborn. Remove the old flush mechanism from the tank.
Install the new flush mechanism according to the manufacturer's directions. Install the rubber gasket on the inside of the tank and the washer on the outside. Install the jam nut. Do not over-tighten the jam nut, as you could damage the tank.
Install the new ballcock into the hole inside the tank. Install and tighten the jam nut on the outside of the tank with the wrench. Do not over-tighten it.
Place the new tank-bowl rubber gasket in position and carefully lower the tank onto the bowl. Install the new brass screws and gaskets, then tighten them just enough to hold water. Do not over-tighten them.
Install the water supply back onto the bottom of the ballcock and tighten it. Install the flush chain. Hook it to the flapper valve and the flush arm and leave one-half inch of slack in the chain. Turn the water on at the stop valve and allow the tank to fill. Look for leaks and make sure the tank fills to the correct water level. Exact float adjustments will vary, and procedures will be detailed in the kit instructions. Lower the float to lower the water level and raise it to raise the water level.