LM317 is a voltage regulator that can also be set up as a constant current regulator. The datasheet will give you more information, or you can google "DDL driver" to find Rog8811's basic writeup on setting up this driver circuit.
Now, your diodes. Since you found two of them, we know that you took apart a DVD burner. The red diode, ~660nm wavelength, is for DVDs; the infrared diode, near 780nm, is for CDs. The IR diode you can save for practicing soldering or something like that. The red one is the one you want. However, as you will notice, they both look exactly alike. Maybe you can post pictures of the heatsinks they are in and we could maybe tell you which is which. Other than that, you could power each diode up using maybe a 1.5V alkaline or a nice variable power supply set to constant current, so you can ramp the current up slowly. Perhaps it would help you to know that most red diodes have ~the same Vf, and red and IR diodes have the same pinouts. The red diode will put out lotsa red; the IR diode will put out what looks like a little bit of red, but what is actually a LOT of near-IR. DO NOT DIRECTLY OBSERVE THE DIODE OUTPUT Instead, point the diode away from yourself and others for testing.
Now, there is a correlation between DVD write speed and the red diode's maximum output power. The higher the DVD write speed (i.e. 1x, 2x, 4x, 8x, 12x), the more power the red diode will be capable of. I've only worked with readers, which aren't good for too much power, and I believe 8x or 12x red diodes, which can put out around 300mW.
In the end, just be safe. Unlike LEDs, these are, for most intents and purposes, powerful point sources of light, and as such, will focus back down to a point source on your retina. Try only to view the light indirectly, i.e. when you are testing the diodes to see which is which, point the diode away from yourself or others, and just put paper in front of it and see what color light is cast onto the paper.
The forum mentioned by another poster here has tons of information strictly about lasers as they relate to the hobby of laser pointers.