For older models, it wasn't hard to detect when your fuel pump was going out, and it was almost as easy to replace. There were two spots where you can find the fuel pump, either somewhere near the underside of the block, or attached to the head, near the camshaft. How these pumps work is that the pump unit consisting of a one-way valve, and a diaphragm that moved up and down with a pump handle, mounted inside the block, resting against a part of the crankshaft. When the crankshaft turns, it makes the pump handle move up and down, pumping fuel from the tank to the carburetor.
These car parts weren't very hard to replace, and the main thing that usually went wrong was either the handle mechanism, or the internal diaphragm. You could tell right away, loss of fuel to the motor, the heavy smell of gasoline, and you could actually see gas spewing out from the little breather hole. The whole unit can be removed with some open-end wrenches, and disconnecting the fuel lines. In front wheel drive vehicles, the manual fuel pump would be located by the camshaft, and the movement of the camshaft would make the pump work. You could find car parts to replace the pump at your local junk yard, as well as order them brand new. You should always replace things like fuel and oil pumps, or alternators, brand new, or refurbished in some cases, never from a junk yard.
Now when electric fuel pumps came out, there were ups and downs to them. One the high side, fuel pumps were now fully internal, and had now outside components, other than the fuel lines, and the electrical connections. You never had to worry about the diaphragm going out, or the rod arm breaking. The problem was, for some stupid reason, someone thought it was a better idea to put the pump unit in the tank, and the idea probably was that now that the pump was electric, it could be placed as close to the source as possible.
The flip side was that the only way to tell that it was going out was when it actually failed. Sometimes, for whatever reason, it was actually the wiring that failed, not the pump itself. The only way you could tell that something was amiss, other than you couldn't get your vehicle started, was that electrical fuel pumps could be heard working. You could actually hear it whirring, if it was working.
Instead of having to pull the whole fuel tank off to get at the pump, you can pick up inline pumps, that totally by-pass the main pump, and is placed along the firewall in the engine compartment. You connect the fuel lines, and connect it to a power source. If you don't know how to tie it all into your wiring system, so it only came on when the motor was started, you could put a kill switch, somewhere either close to the battery or mounted somewhere in the dash. Newer vehicles with fuel injection have a slightly different fuel delivery system. Fuel comes out from the tank, through the pump and filter, up to the fuel injector rail, then into a fuel pressure regulator and back into the tank. These systems are more complicated than the older car parts, and you have much more to deal with diagnostic wise.
First thing you should do when trying to locate the fuel problem is turn off the vehicles motor, then turn the key forward, If you can hear a whirring sound or an electrical motor sound, chances are your pump is fine. Next you need to check your fuel filter, located either near the tank itself, or somewhere along the line near the motor. The filter will usually be made from a hard clear plastic, and if you can see the little filter inside, it needs to be replaced. If this is all right, then you would continue along the line, to the fuel rail and see if you have problems there, or with the fuel pressure regulator. If you still can't find the problem, it may be best to have a mechanic look into it.
If you need an inline fuel pump, fuel filter, or anything else, you should first go to your local car parts retailer. With the computers they have, they can usually find the parts you need, even if it is an older model vehicle.