Removing the alternator in a Chevy Malibu is a pretty simple process.
The first step is to disconnect your battery. To disconnect your battery just remove the negative terminal first using the appropriate socket and then the positive terminal. Then, make sure that the leads are away from your battery terminals.
The next step is to loosen the serpentine belts from the pulleys.
In the photo above, you can see the serpentine belt as its routed around the various pulleys. I have outlined the alternator and the serpentine belt tensioner. (Side note: If you notice the bracket with four bolts in the center-bottom of the photograph below. This bracket mounts the engine to the frame of the automobile. If you need to replace your serpentine belt, you will need to remove these four bolts (with the engine supported of course) in order to slip the serpentine belt below this bracket, but this is another blog post for another day.
The serpentine belt tensioner is spring loaded to keep the serpentine belt tight enough that it wont slip off, but also allows the belt to vibrate and flex as your cruising at high speeds. In order to remove the serpentine belt, you need to purchase a breaker bar. These cost $10-20 dollars. Go buy one. In the photograph above, I also tried to outline the area that you will insert your breaker bar. From here, you can use leverage to rotate the arm of the belt tensioner against the center it is mounted at by applying pressure in the right direction of the breaker bar.
In the diagram above, the belt tensioner is represented in black and the breaker bar in blue. By applying pressure to the breaker bar you should release tension on the serpentine belt and should be able to slip it off of the pulley on the alternator.
If you decided that you want to save $10-20 dollars and not purchase a breaker bar, then you can use a non-racheting socket and some sort of cheater bar in order to get the required leverage needed. This can be a length of pipe or another socket.
Belt Tensioner
Inserting the non-racheting socket in the belt tensioner
socket inserted into the belt tensioner
Second socket placed over the first in order to generate the torque required
Now that the serpentine belt is loosened, you can begin removing the alternator.
To remove the alternator, unscrew the three bolts that mount the alternator. The photograph above indicates where the three bolts are.
In this photograph, the alternator has been removed. Now you can see the three mounts that are used to secure the alternator as well as the various connections that need to be removed. The one labeled wire is the charge wire that is bolted to the alternator from the battery. The one labeled connector with the yellow band needs to be unplugged from the alternator. The one labeled connector that is on top, does not need to be unplugged, it just needs to be slipped off of the mount that is connected to the alternator.
That's it. Your alternator is removed. In order to replace your alternator, do everything in reverse.
Good job!