Building a laser driver circuit?
It has 3 pins on it and my first question is what function does the third pin have?


Many laser diodes are packaged with a photodiode that receives the light from the laser's back facet. This allows setting up a control loop to drive the laser in a constant output power mode rather than just setting a constant current. 

Usually the laser and photodiode are connected in either "common cathode" or "common anode" configuration, so that only 3 pins are needed for the two devices. 


  How do I go about determining the function of each pin safely without damaging it?


The best way is to read the datasheet for the part. Obviously when you're salvaging parts you might not be able to do that. In that case, you have to basically diode-check each combination of pins to find the laser anode and cathod and the photodiode anode and cathode. You can probably tell one from the other because the laser ought to emit at least a small amount of light when you find its pins. Preferably use a diode tester that is voltage limited to maybe 5 V and current limitted to a couple of mA.


  in a driver circuit for a laser I need to regulate not only voltage but current as well. 


For a laser diode, you generally want to drive it with a constant current source. However you should design the source to have a maximum output voltage consistent with the laser's maximum ratings to avoid damaging the laser during power up, power down, or in case of a current-control failure. 

Even better, if your laser does have a monitor photodiode, is to control the supply current to achieve the desired output power level. Again this circuit should have appropriate current and voltage limits to avoid damage.

You might also want to design your supply circuit to have a "soft start" feature to eliminate high inrush currents when turning the laser on and off. (This is probably the reason for the 10 mF capacitor in the schematic you posted)

Final note: 100 mW is more than enough to cause permanent eye damage if you mishandle the laser. Be sure you understand the risks and take appropriate safety precautions before powering up this device.