Note: What I am calling the "ground" is commonly referred to as "earth" in the UK. You may run across texts that follow this convention.
You can think of a ground as an "sink" that electrical noise runs down. If your sink is stopped up or there's something in the drain, then you're going to hear an annoying hum or buzz, much like you do already when you have a single coil pickup selected by itself, only much louder. Often, you can act as the ground by touching the guitar strings if you have a loose wire somewhere.
The sink analogy also holds when you are talking about sending a signal to ground, as when you tap a coil. That is, you figuratively pour the signal from one of the coils down this "drain" so that you are left with a single coil. Follow the circuit on the coil tap page and see for yourself.
|How to properly ground
Ideally, you will want to have all electrical connections that run to ground meet at a single point. Typically, this is the back of one of the potentiometers, since the shells should be grounded as well.
In the picture at left you can see where the back of each pot was neatly grounded with a daub of solder. I'm never this tidy!
What you DO NOT want to do is end up with a ground loop. No matter how good the connections are, everything should independently lead to one location, then out to the ground side of the jack. If you can take two paths from any single point to the jack, you have a ground loop.
In the diagrams below, the three wires represent any connections heading to ground from the pickups, pots, whatever. Note that they converge on the back of the volume pot (typically, this is the most accessible on a strat), then continue along one path to the output. Once you start adding in some of the electronic mods described on this site, you end up with a lot more connections to be mindful of, so it won't always be as simple as I pictured it here.
|Beware the dreaded ground loop!|
Ground loops have a nasty way of sneaking into your work. One way to avoid this is to always sketch things out on paper before you pick up your soldering iron. This will give you a chance to look things over first. That is, provided you stick to the plan!
|The string ground
A string ground is an orphan connection to the rest of the circuit to (usually) the spring claw (see the blob of solder in the middle of the claw at left). If you do not add this into the circuit, you will be left with a lot of noise. Many circuit diagrams (mine included) do not bother to include this, so you absolutely must take care to remember this connection or you will just have to take everything apart again to solder it in place.
If you have any noise and you are certain you have soldered everything properly, go back through with a multimeter and check the resistance of, first, various points in the circuit, then the entire circuit (except for pickups as these naturally have some resistance; make certain the pots are all turned to zero as well, although that depends on which side you are testing from).
Also, try another guitar, cable, amp, etc. Because it is ultimately just another part of the circuit, a bad cable will sound exactly like a faulty connection in your guitar. Thus, the buzz should be canceled or at least attenuated when you touch the strings just as well. If the noise goes away when you try another set-up, you can then begin to isolate the culprit from among your equipment.