It's a real pain. It can be done though. I recommend you have a service manual handy, at least to get the torque specifications.
The Bentley manual would have you take the bumper cover off, then remove the radiator support and swing the radiator, ac condenser, bumper structure all off to the side. That seems like a lot of work, but might allow direct access to the alternator.
You can however get the alternator out from below (not above, the intake manifold will be in your way). These steps are from memory and will not apply to the 4 cylinder models.
First get the car in the air, either jackstands or ramps. Now that the car is in the air you must remove all the splash shields from under the motor.
REMOVE THE NEGATIVE CABLE FROM THE BATTERY TERMINAL...or both if you like. The last thing you need is some sparking while you're working or to ruin your new alternator.
Remove the cover from the side of the engine (skinny one that covers the belt, you don't need to remove the larger one holding the spark plug wires).
Remove the serpentine belt. (Is it time for a new one?) This is done by putting a M8x1.25 bolt in the top of the tensioner to release the tension. Only drive the bolt in enough to remove the belt. I prefer not to keep the spring under compression so let the bolt out afterwards, might as well leave it in part way though. Now remove the tensioner (blocks a bolt for the alternator. 3 bolts, 13mm, one super hard to get at.
Now it's time to go under the car again, remove the power steering pump and the AC Compressor. Remove the power connector(s) on the AC Compressor Clutch first. The P/S pump is pretty light, but you might want something to support the AC Compressor.
You can now get to the alternator, remove the electrical connections first, now the bolts. Some bolts might be easier from above. By this time you might want an assistant. After the bolts are out you'll be wondering why it didn't fall on your face, yeah...it'll take some work, and it's going to be a tight fit.
Now compare your old alternator to the new one...make sure the pully on your new alternator is correct (7 spline belt, not 6 like the 4cyl cars). Mine was incorrect and I had to move the pully, requiring a 12pt driver set to hold the spindal. You don't want to install the alternator more than once if you don't have to, so check now.
--BREAK TIME-- drink a beer, get one for your friend that agreed to help too.
Okay...you're half done and it will go a little faster now because there's going to be a little less fighting with stuff. Now, back under the car!
Alternator goes back in, connect the cables.
AC goes back in, connect the cables.
P/S Pump goes back in.
Put the tensioner back in, don't over torque, it mounts to the head, and it's aluminum, you can strip it out without realizing if you're not careful (ask me how I know).
Tighten that bolt back into the tensioner (you left it in so it didn't roll away right?) Install the serpentine belt (don't remember the path? shame on you, search theor figure it out, it's not hard). Remove the bolt, put it in your tool box for next time.
Reconnect the battery. Start the car. Battery light should go out, lights aren't flickering? If so it looks like you succeeded, congratulations! Turn off the car.
Put all the splash shields back on underneath and the engine covers on top.
Lower the car. Clean the garage. Drink more beer or go driving...
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