When in doubt, disconnect the battery! There isn't anything written here telling you to do anything that causes sparks, but heck, we are near the gas tank. Use your head! Don't call me if you short out something while taking ohm readings under the dash!
This is going to be a real short and to the point. As far as I know, all GM fuel gauges work the same way (except for the new stuff with digital dashes and computers).
I'm assuming that you are using the stock GM sending unit (and maybe an aftermarket gauge)!
What you need to know and recommendations;
1) If you don't already have, and know how to use, an ohm meter, buy one! Have somebody show you how to use it, even if it's some silly computer nerd that doesn't know anything about cars. You need to know this stuff!
2) Buy the factory wiring diagram for your car! If you are "on the cheap", you can get just the wiring diagram and not the full factory manual. If you are really cheap, you may be able to find it at the local library (you may have to ask if there is a certain branch that carries a large automotive section).
3) You have to use a GM gauge or after market gauge that is built to match the GM sending unit! If you go out to buy a new gauge and it doesn't say that it's for GM (or also lists Ford), it will not work!
4) GM fuel gauges work by knowing that the sending unit will provide a resistance (ohms) of zero when empty and 90 when full. That's the reason that you can't use a Ford gauge (Ford sells a fantastic looking gauge>
5) As stated above, the sending unit should show a resistance of zero to 90 ohms. The way that a sending unit works is that there is a coil that has a sweeping contact. That coil can get shorts or can totally break. Shorts can cause the sending unit to cause "jumps" as you go from full to empty or even limit the total range.
6) The sending unit has to have a good ground connection. At the sending unit, you should see a small wire that is connected to the frame. It has to be there and the connection can not be corroded!
7) The wire that goes between the sending unit and the gauge has several connections within the loom. Any one of these connections being corroded will lead to problems. (I know that there is a poor connection somewhere in my 64 wagon. I just haven't had the time to locate it)
8) The gauge needs a 12 volt supply when the ignition is turned on. (If you have other gauges that share this supply, do they also act wrong?) The gauge also needs a good ground reference! (does the gauge work differently when the dash lights are on? they may share the same ground reference.)
9) Here are the steps that I'd recommend if your gauge isn't working;
a) Start with the gas tank as empty as possible.
b) Under the car, remove the wire at the sending unit and use your ohm meter to read the output of the sending unit. Have the reference connection of the ohm meter connected to the frame! It should read near zero ohms. Write down the reading! The reason that you remove the wire is so that you are not reading through the gauge! (also, you should be careful how you hold the leads of the ohm meter so that you are not reading through your own body)
c) Also while under the car, you should check that the body of the sending unit has a good ground connection!
c) Reconnect the wire at the sending unit and then get under the dash. Disconnect the wire that goes to the gauge and then use the ohm meter to read the wire. (disconnected for the same reason as before) The value you read should be close to the reading that you wrote down in step "b". It will be a slightly higher value due to the resistance of the wire and connections.
d) Reconnect the wire and go fill the tank.
e) Now do the same thing that you did in step "b". This time the ohm reading should be around 90 ohms. Write down the reading.
f) Do the same thing as in step "c". The value should be close to the same one you wrote down in step "e".
g) If everything checks out so far, you have narrowed it down to the gauge or it's 12 volt and ground reference.
h) If you think that it may be a ground problem, you could take a wire, attach it to a good ground and then touch the wire to the body of the gauge. (Don't touch anything but the gauge body!) While you are doing this, have a friend watch the gauge to see if it comes to life. Some gauges (like Autometer) have a terminal that needs a ground connection and grounding the body doesn't effect the gauge function!
i) If you think it's a 12 volt problem, you will have to use the ohm meter (on the voltage setting) to check if 12 volts is present at the gauge.
That should cover it!