First disconnect the battery (I disconnect the positive side). Then there are two wires/cables. One is just that, a wire, held by a 10mm nut. Don't lose the nut. The cable has the usual thing you press on to release it and then pull it loose. Mine was very much stuck after 20 years and lots of heat. Be careful not to break old fragile plastic! I had to wiggle it with pliers, while holding down the release tab. When I replaced it, I lubricated it with dielectric grease.
Now for the hard part. It would be easy if the engine wasn't jammed down in the engine compartment. Loosen a 12mm nut, then back off the belt tensioning nut. I have to use a long extension with a U-joint to work the tensioning nut. Nothing will happen probably until you also loosen the 14mm pivot bolt. Then remove the pivot bolt and the bolt that connects the tensioning mechanism to the alternator. At this point the alternator is loose and your challenge is to maneuver it out of the vehicle! You can cheat and remove the fuse fox that is in the way, but it is more sporting to wrestle it past various hoses.
As they like to say, installation is the reverse of removal. Ha ha. The trick is figuring out which of 2 ways the tensioning mechanism gets reassembled. Either guess, get it the wrong way first, then have to do it twice, or see if this makes sense. The bolt that threads into the alternator goes as far away from engine as possible.
Tighten the belt, connect all the electrical stuff, then the battery again and figure out how to reset your radio, and you are in business.
Tom's Camry pages / tom@mmto.org