This came out of a conversation that I had with someone. You should download the FSM on this site if you don't already have it, as I reference it by page. There is probably excess info in there because I was answering a specific question, but you will get the idea. Here goes:
OK go to page 581 of 784 (EL-6). It has the pics of relays with their electrical diagrams. Lets go with the simplest version, the blue one, the pure relay.
OK this is really cool! lol. Its really the basis of many things electronic, and used in many applications on the S12. In the pic, column 1M, you see that the terminals are labelled 1, 2, 3, and 5. What the hell happened to four is a mystery lol. What is even more badass is that if you unplug the relay those numbers are actually molded into the part right by the metal terminal! Anyhow, notice that 1 and 2 are connected by the winding coily looking wire. And notice that 3 and 5 WOULD be connected if that bar was touching the two round dots. What happens is this

When an electrical current flows through a coil of wire (what we see there) it creates a magnetic field which pulls little metal bars towards it. What then happens is terminals 3 and 5 are connected and the circuit is complete!
SO basically, 1 and 2 are the switch side. You flip the switch, in this case the ignition, and 12V go through the steering column into that coil of wire and to ground (lets just assume that is #2). Then say #3 has 12V to it all the time, through a fuse, and now that bar is pulled to connect the #3 and #5 terminal, and 12V can flow through the relay out of #5 terminal, which would usually be electrically dead. Where does it go?? Anywhere, starter, headlights, power antenna, anything really

The ground from there is after the device the relay is controlling. All the relay does is allow power to be SENT to a device, so....
THERE HAS TO BE A GROUND ! Relays can work, but say for example the ground wire for our headlight is fubar, then the headlight has its 12V power but it has no where to go, so no light. This is why it is critical to have power AND ground both working good.
Now what is really cool here is that you can configure the relay to do other things, I'm sure you've checked out the other pics on that page. You can use it to send power to one OR another different place (1T), use it to send power to two different separate circuits at the same time by the same switch(2M), or activate one circuit WHILE taking power away from another (1M-1B). Take a look at those, the black and gray ones, and tell me what they could be used for.... correct! The headlight up/down circuits, power UP, Now OFF, power DOWN, etc. That is what all of those relays on the other side of the car are for

Alot of extra, really.
This is why I love Nissan lol. You don't need this book to check these, now that you have the knowledge of how they work, why? Because Nissan was actually cool enough to have those pics engraved into the mold for the tops of the relays, and have the terminals labelled underneath so we know which terminal does what

Its great, really. I don't know of many car mfgrs that do this.
But on from the bla-bla. What is important to you is whether the damn thing is working. Your first clue is that it clicked, good. That means power SHOULD be getting through the switch side of the circuit, from the ignition switch, so power should be going through the relay out to the computer. (notice how there are other wires there, power is going to other places, like the fuel pump.) WHAT you have to do is this: Armed with this knowledge, use the voltmeter you have to check the relay. Make sure that the coil part of the relay has power going through it (call me if you aren't sure how to set this up, its hard to explain) and that when it is powered up, that power is flowing through the other terminals of the relay (where the bar would connect them in the electrical diagram). If you flip to page 173 of 184 (EF&EC-59) it goes over how to look at the computer
connector and EFI relay and test them. I would think there would be more than one power supply, but...? Either way, this test is done with the plugs disconnected from the ECU. Very important. Also, before disconnecting the computer from the harness make sure the key is in the 'off' position and then disconnect the battery. Other ways of doing it can cause harmful voltage spikes to the computer.
There are many things in a circuit that can go funny resulting in poor performance, really other than what they have listed. Things like- the connector is not firmly mated with the computer/other connector, the metal pin is not firmly touching its mate, the wire is loose/breaking where it connects to the metal terminal, the wire has internal damage along the line (a killer to find if the car has been thru an accident and its hidden by the repair), the ground has corrosion slightly between the ring where the screw passes through and the body, etc., etc., and so on lol. Really tho Nissans are built pretty well, and wierd shit problems like these don't really happen as much. It of course depends on the particular car and history, which is always a bit of an unknown. The key to finding these unusual problems is the voltage drop test, which is easy and simple, I can explain it if you like. Next time tho. This is a lot of info, look at it, and come up with some more questions, because this is just a start. Something is in your system, we just have to find it. If you are unsure of any ways of using your meter and performing tests, I can explain that to you as well, because that is paramount in finding the problem. Proper use of those things is essential to get correct results.