I am trying to teach myself flash photography, and I am currently confused about metering modes. In what shooting conditions would each the following metering modes be best-suited? (And why do they work well?)
*Interestingly, combination #3 is actually not available with my setup (Nikon D80 + SB-700).
With TTL/iTTL, the ambient and flash metering are independent. So you can use spot or matrix for your background, whatever is most suitable. So you would probably use matrix most of the time unless you have extreme lighting situations where matrix isn't doing the job. Matrix is best if you want any chance of getting the correct background exposure. If you use spot, both the ambient and flash metering will only take into account that one spot and your background will not be considered.
The flash is controlled by a separate metering system which will attempt to correctly expose your subject (I think it uses distance information from the lens, plus preflashes to measure reflected light off the subject).
TTL/iTTL would be used most of the time, except for one specific situation where you use TTL-BL.
TTL-BL (BL=back lit) attempts to balance the light of your subject with a bright background. In this mode, the camera and flash meters are coupled and work together. But it is only meant to be used in back-lit situations.
I would say the combination of TTL-BL + spot/center-weighted is not available because the meter needs the background information to know how to balance the scene. When you use TTL-BL the metering of both ambient and flash is done together. The matrix metering calculates the correct overall exposure, sets aperture, ISO, shutter speed, depending on what mode the camera is in, then also instructs the flash to fill in a certain amount of light which it has judged is needed to brighten the subject appropriately.
The iTTL system is very smart and usually does a terrific job. But if it's not giving you good results (usually in extremently bright or dim situations), I think the best method is to switch off the flash first, set camera to manual mode, and get the background looking as you want it, with just the ambient light. Then switch on the flash, probably start with minus 1 flash compensation, and adjust the flash compensation until the subject is well lit. The background, which won't be lit much at all by the flash, should remain constant, so you'll get a good balanced image.
There is a complete guide to Nikon CLS here: Nikon CLS Practical Guide
But also see this for an alternative view of how TTL-BL meters from a fellow Kiwi.