Pickup wiring is one of those items that is worth knowing, especially if your bass has two pickups or split-type pickups.
Most pickups are wired in a parallel configuration to the output jack. See the diagram below for two Jazz Bass pickups wired in parallel. This is the normal configuration for a Jazz bass and two pickup basses, like the G&L 2500.
There are some important things here to note. First, the pickups are actually out of phase. When both pickups on a Jazz bass are turned up full-on, the pickups cancel out any hum that may be in the area.
If you use one coil only, it will be in single coil mode, and you can pick up the hum. If you like the sound of only one coil, and hate the hum, try using a split coil Jazz Bass pickup, and wire them in hum-bucking mode.
Dimarzio makes these, and they are a very good-sounding pickup. I have used them on previous Jazz Basses, and they work well. I especially like the adjustable magnetic pole pieces, which are easily adjusted with an Allen screwdriver.
Secondly, the control knobs shown (above) are wired in the Jaco Pastorious preferred fashion: Volume, Volume, Tone. The standard method is to have: Volume, Pan, and Tone.
A very important note here is to ground the bridge. If the bridge is not grounded your bass will almost always hum when you are not touching the strings.
If you still have hum problems you should also have, or should install brass plates under the pickups, and have them connected to the common ground, usually on the back side of the volume and tone pots.
Make sure that these plates do not short out the pickups. You can insulate these plates with electrical tape or some other insulator.
P-Bass pickups are split coil types of pickup. The two coils are wired in series, in most cases. However, you can wire them in parallel too, which will make the sound brighter, with less bass.
The recommended wiring practice is to wire them in series so that the coils are out-of-phase with each other. This practice causes the pickup to become a hum-bucking (hum-canceling) pickup coil.
The advantage of this practice is to make it immune to outside electrical noise, which is a great plus for any bass. Of course, you can change the pickup wiring to the single coil with these, by switching the wiring on one of the coils.
Usually, the coils come with color-coded wire connected to the coil terminals. Some coils use Red and Black, while others use White and Black.
Below is a diagram showing how a standard P-Bass split coil pickup is wired as a hum-canceling pickup. The pickups are wired in series. (For another example of having them wired in parallel, check out pickup parallel wiring.
Notice that the split coils are actually out of phase here. It does not matter in this case that the coils are out-of-phase since there are no other pickups here.
If the coils are wired in-phase, then it becomes a single coil type of wiring, and you can expect to hear a hum when you are near electrical fields.
If you wish to add a J-Bass pickup in the bridge position, you will likely need to wire the P-Bass as a single coil, unless you thought ahead to buy a split coil Jazz Bass pickup, as mentioned earlier.