What exactly is a photodiode?

I am looking for a in depth answer to what a photodiode is and where can I get them.

Remember, photoDIODE, not Photoresistor

It's a diode... like any other diode, although with a transparent package. Sometimes the external package material is tuned for a specific spectrum, but EVERY PN junction exhibits a photo electric effect. Light applied to the junction will produce current through it. The photons knock around the free electrons. Any LED will exhibit a photo diode effect. (Just put one on a scope and shine a light at it) Basic semi conductor physics. Also little known, is all semi conductor junction emit some form of light =) One of the reasons why they come in opaque packages.

.... so if you connect a photodiode in series with a resistor and connect the whole lot accross a dc supply, the current through the resistor (and therefore the voltage accross it) will vary with the light intensity.

With specially made diodes light variations in the MHz region can be monitored. I have used PIN photodiodes to detect laser pulses only about 10ns duration.

still, where can i get them?

Also, by hooking them up to the base of a NPN transistor, could I use them for a light following robot?

A Photo-diode can be used in one of two ways:
1) If it is reverse-biased then it leaks a small current when it is exposed to light or IR. The reverse-bias voltage reduces its capacitance so it is fast.
2) If it has no bias voltage then it generates a small forward voltage when it is exposed to light or IR. It is very sensitive.

Any generic LED can be used as a photo diode. But you need relativly sensative circuits to really use them.

Well I've managed to use a 400nm violet diode to detect 407nm light from a black light using a multimeter so I wouldn't agree, you just need a simply high impedance amplifier.

still i dont get how to use them and where to get them!!!