How to install 6X9 speakers in the rear deck
You are gonna need a few materials and tools before you start:
Jigsaw ($30 at Lowe's)
Powered Handsaw with metal cutting blade (I used a Black and Decker NaviGator)
Tape Measure
Drill w/ drill bits
Hammer
Rubber Mallet
Spray Adhesive (For the carpet)
Utility Knife
A Small sheet of 1/4 inch plywood
A Large, and very strong Flat Head Screwdriver
Sharpie Marker (I used a silver metallic, which worked super well)
Template for the speakers you are going to use
Enough carpet to cover the rear deck (I used Lowe's Outdoor Living Carpet)
SAFETY GLASSES! (I used an old paintball mask)
An abnormal screwdriver that can get to the speaker screws that are only an inch or so under the window (Below the sharpie in picture)
Some kind of wrench
It sounds like it takes a lot, but aside from the carpet, adhesive, wood, and jigsaw, these were all things that I found around the house. And throughout my explanation I'm probably going to point out some obvious details, not to dumb it down, but because I overlook some random things myself.
NOW, on to the whole procedure:
Step 1.) Remove the back seat.
This can be a little tricky. First thing you need to do is remove the 3rd brake light cover. Once you get that off, take the light (NOT just the light-bulb, but that whole little piece) out of the assembly. Unscrew the two bolts at the bottom of the assembly, and remove the assembly. If your Corolla came with factory speakers, you're gonna need to remove those. Now you need to pull the rear deck out. This is gonna take a lot of fidgeting, but do not be afraid to break the wood a LITTLE BIT. Remove the plastic seat belt guides when you are able to.
Step 3.) Separate carpet from the wood
Before you can do this you're gonna need to remove all the plastic things that are attached to it. The hinge covers can be removed by drilling out the rivets that hold it on (From the Back-side). Be careful not to drill all the way through to the front, as you may (I didn't) want to use them on the new deck. Once all that jazz has been removed, find a point on the carpet to start peeling it away from the wood. Pull slowly, and make sure no broken pieces of wood stay behind on the carpet.
Step 4.) Trace the old rear deck (Using the wood, not the carpet) onto the wood you are using for the new deck
This step is pretty simple, and explains itself, but I do have some things to add. When I bought the plywood, I didn't measure it out first. The new piece of wood ended up being about three inches short, and that actually helped me out quite a bit in fitting the new deck. If you do the same thing (Buy a short piece of wood), all you need to do is line up one side, and trace it from there. After you cut it out, there will be plenty of scrap to finish the deck. Test fit the new deck, and once it fits right, move on. Do not cut the speaker holes yet, that will be done AFTER you cut the carpet. I suggest making the top of the deck (Near the 3rd brake light) about 1/4 inch shorter, because your carpet is most likely going to be thicker, and your wood is about twice as thick. I didn't do that, so you don't have to, but I definitely suggest doing so.
Step 5.) Carpet the new deck
Put the carpet down on the ground, and put the deck on it, with about an inch of carpet showing on all sides. Use the utility knife to cut it out. Spray adhesive on the deck and the backside. The adhesive I used (DURO All Purpose Spray Adhesive) requires that you let it dry for one minute before gluing the materials together. I found that waiting three to five minutes works the best. Make sure that there are no bubbles or flaps on the top. Now glue all of the edges using the same technique, cutting the excess around the corners. If you have a staple gun handy, staple very lightly around the edges. This will make the staples easy to remove, and they will hold the carpet in place while the adhesive sets.
Step 6.) Cutting and hammering the metal deck
You must use something to protect your eyes.
This is the most important thing to remember!
This is where the powered handsaw comes in. I found that the flats right near the 3rd brake light are the best location for the speakers. I really tried to put them in another location first (As you can see in the picture), so I know for sure that this is the only practical location for the speakers. First thing you need to do is draw lines where you want to cut, using the sharpie. You want to cut out as much of that section as possible. In the picture below, it shows my lines. The line closest to the window marks where the is a little support tacked to the underside. Now, to get a place to start, hammer that strong screwdriver into the metal starting at one of the holes. It is very easy to do, and is very quick.
You can use any technique to cut it, and here's the way that works best for me: Start from that hole and cut to the four corners. Hammer the now flaps down, and cut them off from inside the trunk. The wrench will help out a lot, here and there, bending the metal where the hammer can't. After you get to majority of the metal out of the way, you're probably gonna have to hammer the sides of the of the metal to make the hole even bigger. Feel free to cut some more to make this possible. At some point, you're going to have to cut the little guide for the trunk torsion bars. It has not affected the functionality of my trunk whatsoever. What I did, was cut the bracket (guide, whatever you want to call it) at the welded point nearest to the rear bumper. I just folded it under itself toward the back seat, and viola.
(This picture was taken from the backseat)
Once you get the holes pretty large, put your speakers down in the holes, and make adjustments accordingly. This is going to take some estimation and consideration, so do not be in a hurry to cut the speaker holes in the wood. You could likely end up making another whole deck. Once you decide exactly where the speakers will go, make sure, that grilles and all, they fit with the cover for the 3rd brake light.
Step 7.) Cutting the speaker holes in the wood.
Put the new rear deck in the car. Make sure it is in tight, and exactly where it will sit when completely finished. Get in the trunk and trace onto the bottom of the wood deck, as close to exact as you can, the area of metal you cut out. You are going to use this as a reference location. Now take the new deck back out. Put the speakers in the metal holes where you want them, and try to picture where they will sit in the wood. The last thing to do before cutting is to trace the template for your speakers onto the backside of the wood. Now cut the holes, and the jigsaw will cut the carpet easily and cleanly.
Put the wood deck back in its place under the window, and drop your speakers into the holes you just cut. If you did everything right, they should fit, or just about fit in perfectly. If needed, hammer the metal in some more, until your speaker don't touch the metal deck. Screw them in, and your done.
I'll add more pictures and update a little bit over the next few days.
You are gonna need a few materials and tools before you start:

Jigsaw ($30 at Lowe's)
Powered Handsaw with metal cutting blade (I used a Black and Decker NaviGator)
Tape Measure
Drill w/ drill bits
Hammer
Rubber Mallet
Spray Adhesive (For the carpet)
Utility Knife
A Small sheet of 1/4 inch plywood
A Large, and very strong Flat Head Screwdriver
Sharpie Marker (I used a silver metallic, which worked super well)
Template for the speakers you are going to use
Enough carpet to cover the rear deck (I used Lowe's Outdoor Living Carpet)
SAFETY GLASSES! (I used an old paintball mask)
An abnormal screwdriver that can get to the speaker screws that are only an inch or so under the window (Below the sharpie in picture)
Some kind of wrench
It sounds like it takes a lot, but aside from the carpet, adhesive, wood, and jigsaw, these were all things that I found around the house. And throughout my explanation I'm probably going to point out some obvious details, not to dumb it down, but because I overlook some random things myself.
NOW, on to the whole procedure:
Step 1.) Remove the back seat.
The bottom portion comes off first, and has two little tabs right under the cushion, just pull them away from the seat. After that's off, the upper portion can be removed by unscrewing the two bolts at the bottom. If you have a socket set, the size of the bolt is 12 MM. If not, just use any wrench you can find to do the job.
Step 2.) Remove the Rear Deck
This can be a little tricky. First thing you need to do is remove the 3rd brake light cover. Once you get that off, take the light (NOT just the light-bulb, but that whole little piece) out of the assembly. Unscrew the two bolts at the bottom of the assembly, and remove the assembly. If your Corolla came with factory speakers, you're gonna need to remove those. Now you need to pull the rear deck out. This is gonna take a lot of fidgeting, but do not be afraid to break the wood a LITTLE BIT. Remove the plastic seat belt guides when you are able to.
Step 3.) Separate carpet from the wood


Before you can do this you're gonna need to remove all the plastic things that are attached to it. The hinge covers can be removed by drilling out the rivets that hold it on (From the Back-side). Be careful not to drill all the way through to the front, as you may (I didn't) want to use them on the new deck. Once all that jazz has been removed, find a point on the carpet to start peeling it away from the wood. Pull slowly, and make sure no broken pieces of wood stay behind on the carpet.
Step 4.) Trace the old rear deck (Using the wood, not the carpet) onto the wood you are using for the new deck
This step is pretty simple, and explains itself, but I do have some things to add. When I bought the plywood, I didn't measure it out first. The new piece of wood ended up being about three inches short, and that actually helped me out quite a bit in fitting the new deck. If you do the same thing (Buy a short piece of wood), all you need to do is line up one side, and trace it from there. After you cut it out, there will be plenty of scrap to finish the deck. Test fit the new deck, and once it fits right, move on. Do not cut the speaker holes yet, that will be done AFTER you cut the carpet. I suggest making the top of the deck (Near the 3rd brake light) about 1/4 inch shorter, because your carpet is most likely going to be thicker, and your wood is about twice as thick. I didn't do that, so you don't have to, but I definitely suggest doing so.
Step 5.) Carpet the new deck
Put the carpet down on the ground, and put the deck on it, with about an inch of carpet showing on all sides. Use the utility knife to cut it out. Spray adhesive on the deck and the backside. The adhesive I used (DURO All Purpose Spray Adhesive) requires that you let it dry for one minute before gluing the materials together. I found that waiting three to five minutes works the best. Make sure that there are no bubbles or flaps on the top. Now glue all of the edges using the same technique, cutting the excess around the corners. If you have a staple gun handy, staple very lightly around the edges. This will make the staples easy to remove, and they will hold the carpet in place while the adhesive sets.
Step 6.) Cutting and hammering the metal deck

You must use something to protect your eyes.
This is the most important thing to remember!
This is where the powered handsaw comes in. I found that the flats right near the 3rd brake light are the best location for the speakers. I really tried to put them in another location first (As you can see in the picture), so I know for sure that this is the only practical location for the speakers. First thing you need to do is draw lines where you want to cut, using the sharpie. You want to cut out as much of that section as possible. In the picture below, it shows my lines. The line closest to the window marks where the is a little support tacked to the underside. Now, to get a place to start, hammer that strong screwdriver into the metal starting at one of the holes. It is very easy to do, and is very quick.

You can use any technique to cut it, and here's the way that works best for me: Start from that hole and cut to the four corners. Hammer the now flaps down, and cut them off from inside the trunk. The wrench will help out a lot, here and there, bending the metal where the hammer can't. After you get to majority of the metal out of the way, you're probably gonna have to hammer the sides of the of the metal to make the hole even bigger. Feel free to cut some more to make this possible. At some point, you're going to have to cut the little guide for the trunk torsion bars. It has not affected the functionality of my trunk whatsoever. What I did, was cut the bracket (guide, whatever you want to call it) at the welded point nearest to the rear bumper. I just folded it under itself toward the back seat, and viola.
(This picture was taken from the backseat)

Once you get the holes pretty large, put your speakers down in the holes, and make adjustments accordingly. This is going to take some estimation and consideration, so do not be in a hurry to cut the speaker holes in the wood. You could likely end up making another whole deck. Once you decide exactly where the speakers will go, make sure, that grilles and all, they fit with the cover for the 3rd brake light.
Step 7.) Cutting the speaker holes in the wood.
Put the new rear deck in the car. Make sure it is in tight, and exactly where it will sit when completely finished. Get in the trunk and trace onto the bottom of the wood deck, as close to exact as you can, the area of metal you cut out. You are going to use this as a reference location. Now take the new deck back out. Put the speakers in the metal holes where you want them, and try to picture where they will sit in the wood. The last thing to do before cutting is to trace the template for your speakers onto the backside of the wood. Now cut the holes, and the jigsaw will cut the carpet easily and cleanly.

Put the wood deck back in its place under the window, and drop your speakers into the holes you just cut. If you did everything right, they should fit, or just about fit in perfectly. If needed, hammer the metal in some more, until your speaker don't touch the metal deck. Screw them in, and your done.

I'll add more pictures and update a little bit over the next few days.