Your wondering what pins on the photo-transistor to hook up to what? Well, I'm not sure that you could actually use these too well with the NXT as it doesn't handle IR codes but as far as I figured it out the middle pin was the signal and the outer two where for +5V/Gnd. Don't remember exactly which was power, which was ground though... should be fairly easy to figure out with a breadboard, a transistor (2N3904 or similar), a couple resistors, one of the little IR LEDs you pulled off of the board and a little red LED. I'll work on figuring out which is which when I have time (in about a week
Caps are a fairly basic/important piece in electronics. Think of them as rechargeable batteries. If you apply a voltage like 1.5-2V to a AA rechargeable battery it will charge. Lower that voltage so that it is less than the battery's and the battery will stop charging. If you have something like a DC motor being powered by the battery it will wear down the battery. Apply 2V, it charges again.
A cap is in many ways the same. However, they have much less capacity than a rechargeable battery. The blue cap on the board is probably 47-100 uF. That could power a LED for a very short time, maybe 0.3-0.7 seconds before it would discharge completely, depending how much electricity your LED used. The other caps would only power your LED for a couple hundred micro-seconds or less.
Caps have many other uses, search them up on Wikipedia or Google. You will find some very in-depth explanations. It does come in handy to have a parts drawer full of random values of caps; save them!