The fuel pump circuit is fairly easy. (hah) It's only intimidating for a little bit, then it starts to make sense, believe me.
Essentially, there is a 12V wire from the battery to the fuel pump relay. This is where the power for the fuel pump comes from.
There is another wire FROM the relay that goes to the fuel pump. This is where the power from the battery goes to the fuel pump.
Think of the relay as a light switch. When the ignition is off, power is going to the switch (relay) but the switch (relay) is "off", so the 12V from the battery goes nowhere. When the switch is "on", the 12V goes from the battery, through the switch, to the pump. That make sense?
Now, to make it a bit less complicated than it actually is on the truck, instead of the relay being like an actual light switch, the "on/off" is controlled via two additional wires. So you've got 4 wires at this point: 12V battery wire to the relay, 12V wire to the pump, and these two.
These two wires are what controls the on/off portion of the relay. One of these wires has 12V only when the key is in run/start (so the pump will never run with the ignition off) and the other one is a ground wire. But instead of just being connected to ground, it is connected to yet another "switch", and that switch determines when the pump should run.
(In a correctly wired/working fuel pump circuit) You have 12V ALWAYS going to the relay from the battery. When you go to start the truck (turn the key to run or start) the ECM grounds that switch wire. Grounding that switch wire operates the relay, and connects the 12V battery wire to the wire to the fuel pump. Thus, the pump gets power.
If someone has a link to a relay wiring diagram that is simple (like a fan setup) then I think it would make a bit more sense to look and read. But it's that simple...4 wires...two provide power to the pump, the other two wires tell the relay when to give power to the pump.
Yes, simplified, but it gets the point across I hope. You need to check for 12V going to the relay first off, from the battery. One of the 4 wires, key off, should have 12V to it. Then you would check your relay connector for 12V when the key is turned to "run". Now there should be two wires with 12V going to them.
It could be as simple as a bad fuse for the fuel pump, or a bad wire at the relay connector. Not sure that all TBI relays look the same, but mine is rectangular. There should be a RED wire hanging off the connector that is not hooked to anything, that is a test wire. (put 12V to it, you should hear the pump running)