Interestingly, I did pick up on his description of a "small" diode as meaning something like this:
The 1N400x diodes are probably the most popular diodes around. They are all rated at 1 Amp. (The high resistance values in your circuit will keep the current far below 1A.) The 1N4001 has a PRV (peak reverse voltage) rating of 50V, the 1N4004 is rated for 400V, and the 1N4007 is rated for 1000V.
I usually buy the 1N4007, since they are all very cheap* and about the same price. But, any of the 1N400x dioes are perfectly acceptable for things that run at the common low-voltages of 5V, 12V, 15V, etc.
"Regular" silicon diodes have two ratings, reverse voltage and forward current. These are maximum ratings that should not be exceeded.
In the forward direction, the diode "turns on" (starts conducting) at about 1/2 volt. It's a non-linear device, so unlike a resistor, the voltage does not go over about 0.7V no matter how much current you run through it.
in the reverse direction, (essentially) no current flows (assuming you don't exceed the PRV rating ;) ).
Since the diode never "sees" high-voltage and high-current at the same time, it doesn't have to dissipate much power.
If you exceed the reverse voltage it can break-down and start conducting. In that situation, you can get voltage and current at the same time,and you can fry the diode. And of course, you can fry the diode if you exceed the forward current rating.
* I hope you get 5 or 10 in the package for $1.19 USD at Radio Shack. They are 6 cents each at [u]Jameco[/u].