Welcome to Gear Swaps 101.
I wrote this how-to as a guide to help anyone through this process. I am performing the install on a 1993 Firebird Formula, and while all 4th gen f-bodies came equipped with GM's 10 bolt rear end, there are a few changes from year to year (mostly in the differential itself). Before performing this install it would be wise to see what kind of differential is in your car, some of the zexel-torsen rears in some LS1 cars require modification to get certain gears to fit. There are many gear choices available, researching on forums will help you decide which is best for you. With that being said, read on.
If you are very mechanically inclined & experienced, have a decent set of tools and a day to spare, by all means give a gear swap a try. It can be time consuming and a little difficult, which is why I generally don't recommend it to newcomers, or even those who do most but not all of the work on their cars. Hopefully this how-to will allow you to gauge whether this is something you can tackle or not. I do this kind of crap all day long on Dodge trucks (which in my opinion are easier to setup since backlash is set by using a tool down the axle tube and not shimming).
To perform this install you will find it is handy to have air tools, especially an impact gun which you will use to remove & install the pinion nut. Since I did this car at my place of employment, I have access to bearing puller/removers that make life much easier...they are available to purchase, or you can try other methods of removal (such as heating/beating/etc). Some of the things you'll need include a basic set of 1/2" drive sockets & driver, 3/8th" driver (for removing gear oil plug), impact gun, pen magnet, dial caliper (for measuring shims), gear paint, 1 1/4" impact socket, 18mm wrench, 11mm wrench, 8mm wrench, BFP (big f**king pry bar), dial indicator gauge, chisel/punch, hammer (couple different sizes), and a couple odd things I'm forgetting.
You have a choice whether you wish to replace all of the bearings, or reuse yours. I highly recommend replacing everything, after all how many times do you take apart your entire rear? It would suck to waste time installing gears and then have a pinion bearing go bad a month later because you were too lazy to change it. When you purchase gears there is often an option of purchasing an 'install kit' for another $90 or so, do it. I get a discount through the dealership and even with my price the total with all of the bearings etc is quite expensive.
The absolute bare necessities include gear oil (75w90 for this car), shim kit, gear oil additive (for limited slip cars), loctite, and RTV gasket maker. If you are replacing everything, you will additionally need: carrier bearings (2), front pinion bearing, rear pinion bearing (all bearings will come with races), crush sleeve, and a pinion nut. You can also do wheelbearings if you please...