This will take some time, so gather up your hand tools and get a cup of coffee...
OK, unplug the washer and turn off the water supply valves to the washer. Now open up the top washer door and pull off the top of the agitator (the fabric softener dispenser on some models). There could be a screw inside holding the agitator onto the transmission shaft, so remove that if present.
To get the agitator to come off the transmission shaft, you might have to rock the bottom edge back and forth, all the way around it, to help loosen it from the tranny shaft. Once you get that off, there might also be a spacer bushing underneath it (a plastic hub looking thing) remove that too.
Once you've go those items off, you can then use a small metal putty knive, about 1 - 1 1/2 inches wide to release the top panel from the cabinet. If you get down and look straight at the front edge of the washer, you'll see two (2) indents where the locking clips are located. Just push in with the putty knive about an inch and it will release. Do this in both places and the top will be able to be lifted up and back exposing the inside of the washer and tub.
Now you can remove the fasteners (screws or hex screws) that are under the hub spacer and that hold the tub onto the transmission. With these removed, you can now lift the wash tub out of the washer cabinet.
Once you've got the tub out, you'll see the wash tub boot. It's held in place with two (2) large diameter hose style clamps. Loosen and remove these with either a 1/2", 5/16" or 3/8" nut driver, (depends on where and when made as to the size that was used).
Once you have the clamps off the boot, you can carefully remove the boot from the outer tub and the transmission body. Once you have the boot off, clean the surfaces of the outer washer tub to remove any gunk that might make the new boot leak. Also, on the transmission side, use the putty knive to carefully scrape around the rim to remove any water deposits that have built up over the years, etc. Get it as clean and free of gunk as possible, again, so the new boot won't leak.
Carfully install the boot around the transmission first and tighten the clamp, now carefully put the boot around the outer tub lip and use your finger along the inside to help get it over the lip. Once it's on, make sure it's lined up and all the way over the outer tub lip and install the clamp. With the clamps, you want them tight, but not so tight that the clamp deforms or the boot gasket gets cut, so go easy and tighten them carefully.
You can now complete the re-installation of the remaining parts and you'll be back in working order in short order. If you wish, before you put all the other parts (tub, hub, agitator, etc.) back in. you can add some cold water to the outer tub to check for leaks, but you should be fine, if you cleaned the surfaces before putting on the new boot gasket.
Here's a link that shows your GE Washer and the parts described. It will help you better understand the repair and lists the parts, in case you need other components, etc. Just click on the "tub, basket, and agitator" link to see the affected parts.
Hope you find this Very Helpful and best regards!