Disconnect the positive battery cable.
Use a serpentine belt tool to loosen the belt and move it off the pulley of the alternator.
Put back the bolts that hold the alternator in place. It will be a minimum of 2, and no more than 4, bolts depending on your make and model.
Employ a socket and ratchet to loosen and remove the bolts.
Pull out the alternator, then unplug and remove the nut for any electrical connections.
Remove the alternator from the engine and take it to the parts house in order to get a new or rebuilt one.
Inspect the new alternator, while still at the parts house, comparing it to the old one. Make sure the voltage regulator and pulley match up to the old one. If it does not, get the parts house to put the old pulley assembly on the new one.
Reverse the process to install the new alternator.
Connect the electrical plugs and wires onto the new alternator.
Slide the alternator into place and begin threading the old bolts in the right position.
Put the alternator pulley back into place, bolting it down. Be sure to check the alignment with the belt tensioner pulley.
Use the serpentine belt tool to get the slack you need and slip the belt back over the alternator pulley. Now release the tool by putting tension on
Reconnect the positive battery cable.
Start up your car and make sure the alternator is charging.