Open the hood, locate the serpentine belt tensioner and move the tensioner off the serpentine belt with the serpentine belt tool. Slip the belt off the tensioner pulley with your other hand and then slowly move the tensioner back to its normal position. You can pinpoint the location of the belt tensioner by following the belt routing diagram, printed on the fan shroud.
Disconnect the negative battery cable from the battery with the battery wrench. Push the cable end away from the battery so it doesn't make contact during the repair.
Turn the lug nuts on the right-front wheel counterclockwise until they're loose enough for hand removal, but leave them on for now.
Lift the right-front end with the floor jack and support it on a jack stand placed underneath the right-front frame. Remove the lug nuts and right-front wheel by hand and set them aside.
Slip the serpentine belt off the alternator pulley by hand. You can access the alternator through the wheel well. Unplug the wiring harness from the alternator by hand and remove the ground strap with your socket set.
Remove the alternator mounting bolts with your socket set. Lift the alternator out of the engine well, through the wheel well. Insert the new alternator in reverse of how you removed the old one.
Thread the alternator mounting bolt through the new alternator and into the alternator bracket by hand. Tighten the bolts with your socket set.
Attach the alternator ground strap with your socket set. Plug the alternator wiring harness in by hand.
Slip the serpentine belt over the new alternator pulley. Reinstall the wheel and lug nuts by hand. Lower the Taurus of the jack stand with the floor jack.
Move the belt tensioner aside again and place the belt on the tensioner pulley with your free hand. Hold the belt on the pulley and slowly move the tensioner back to its normal position. Reconnect the negative battery cable to the battery.