You need to remove the serpentine belt, and disconnect the negative battery cable and set it to the side, making sure it can not move back and contact the battery post.
Then, from underneath, you need to unfasten the bolts that support the A/C compressor- after loosening slightly, you need to smack them sharply on the end with a hammer to reset the sliding nut on the end of each, so that the compressor can be dismounted from the bracket (the nuts are mounted inside the bracket, and slide inward to compress against the body of the compressor to hold it tight). If the compressor does not move easily, the sliding nuts are still sandwiched up against the compressor, and you may need to smack it again. You should be able to dismount the a/c compressor without unfastening any of the hoses (unplug the electrical connector) , and move it out of the way. You will need to suspend it in some way, with bungee cords or ties, to keep from putting stress on the hoses.
The same with the alternator- you need to loosen the bolts, smack them to reset the slide nuts. Remove the electrical connector and the power cable (13mm nut) and then remove the alternator outward toward the fenderwell.
You will likely need to swap the pulley over to the new alternator (or replace the pulley) it is a one-way clutch. It requires two special tools, one to hold the alternator shaft from turning, and the other internal socket to turn the pulley.
Installation is the reverse of removal. Don't connect the battery until after the power cable is on the alternator stud.