Shift down to the hardest gear.
Take a Phillips-head screwdriver and loosen the plastic screw on your shifter.
Remove the plastic screw.
Push the cable completely out of the shifter. The cable end should pop out where the screw was.
Keep the shifter in the most difficult gear.
Slide the new cable through where the old cable came out.
Tighten the screw back down tightly with the Phillips head.
Hook up the new cable into the derailleur from which you removed the old cable.