Ok, let me start by saying that there was nothing wrong with my shifters other than old grease that had gotten very pasty. If that is the case for you as well, or if you're unsure, then I would highly recommend the following:
1. Only partially disassemble the shifter, perhaps as far as getting the assembly out of the brake lever/housing but no further.
2. Degrease it as thoroughly as possible, either by soaking or spraying or some combination. Take a few days for this if necessary.
3. Re-lube it with something thinner than grease. I used tri-flow, you can use whatever you want. Remember, WD40 is not a lubricant (not for long anyway).
If that doesn't work, or if something is clearly broken and needs to be replaced, then you may need to further disassemble the unit. It's really not very difficult at all once you know how it all goes, but it can be very difficult to figure out how it all goes! I fully disassembled my right (rear) shifter, but got smart for the front shifter and went with Plan A.
Kimmo's write up is very helpful. I'm not going to write step-by-step directions, but the pictures will be very helpful, and i'll include a few tips.
The special nut with the 4 slots in it: I was able to remove and re-install that with a large, flat-blade screwdriver.
The main thing to pay attention to is the orientation of all the parts as you take them apart. You want to note which side is facing up, and where they are in terms of rotation around the main shaft.
One thing i got wrong was the order of the two ratchet rings (of course i'm making up all my own terminology here). The thicker one goes on top. Also, pay attention to the orientation. You can see them in many of the pictures.
Another tricky spot was figuring out how the black, horseshoe shaped spring went in. If you look closely at the pictures you'll see its orientation. The pieces above and below it were tricky also, but it's all visible in the pictures.
The pictures were taken as i was assembling the unit from being completely taken apart, but they're in reverse order. So the first picture is the end of the assembly and the last picture is the beginning... don't ask why...
