Recently I managed to break one of the triggers in a PS3 controller such that it wouldn't spring back properly after pressing it. Rather than throwing it out or sending it in to get repaired, I had a go at fixing it myself. The repair wasn't too difficult, so I'll summarise the steps here in case they help anyone else.

I got the information on disassembling the controller and ideas for replacement parts from various sources on the Internet, so this isn't new information. Hopefully it will be helpful having it all together for others who run into this problem though.

1. Unscrew the 5 screws on the bottom of the controller.
2. You will notice that the two halves of the shell don't come apart yet. This is because there is a clip located between the two analogue sticks. If you press the bottom half of the shell between the two sticks, the halves should separate. I suggest doing this with the controller upside down so that the insides stay in place.
3. While the trigger/shoulder button assemblies feel like they can come loose, don't try to remove them: there is a ribbon cable attaching them to the main board. This repair should be possible without removing the trigger assembly, so leave them in place.
4. There is another piece of the shell that sits between the shoulder button and trigger. Remove it on the side of the broken trigger.
5. The trigger is held in place by a metal axle. Using a thin screwdriver, push the axle and slide it out. This should allow you to remove the trigger and the remains of the trigger spring.

At this point, you'll need a replacement trigger spring. One suggestion I found was to use the shutter spring from a 3½" floppy disk. I had a few lying around, so this is what I used. It is pretty easy to snap the two sides of the case apart and remove the spring. Now on to the reassembly:

1. The arms on the floppy shutter spring are longer than those on the original spring, so you will need to cut them to size with a wire cutter. You're probably better off making them slightly too long rather than too short.
2. Position the spring in the trigger and push the axle through the hole on the side of the trigger, just far enough so it goes through the centre of the spring.
3. Now comes the tricky bit. Position the trigger in the trigger assembly and push the axle the rest of the way through to attach the trigger. The tricky part is making sure the spring stays in place while you do this, and may take several tries.
4. Reattach the piece of the shell that goes between the shoulder button and trigger.
5. Check to make sure the shoulder button and trigger feel right when pressing them.
6. Slide the bottom half of the shell back on to the controller. There are some grooves next to the triggers you'll need to guide it over, and then push it together until the clip between the sticks clicks into place.
7. Replace the 5 screws, and then test the controller in a game to make sure all the buttons work.

After the repair, the controller felt as good as new. The tension on the repaired trigger felt slightly stronger than the other one, but not enough to feel weird. If that kind of thing bothers you, you might want to replace both springs at the same time.

I also noticed that the battery was not soldered onto the main board, but rather attached by a connector. This means that it should be fairly trivial to replace when it dies (assuming that I can find someone who sells replacements).