arduino
I have permission to access a (borrowed) Arduino Uno, and the documentation says it can be powered with 3.3 Volts from the 3V3 pin:
3V3. A 3.3 volt supply generated by the on-board regulator. Maximum current draw is 50 mA.
http://arduino.cc/en/Main/arduinoBoardUno
However, I would like to use a 24V DC power source.
The safe range is supposed to be 6V-20V.
If I could get a transformer in place to change the 24V DC to 8V DC, could I apply that 8V to the 3V3 input (without frying the board)?
Jason, I'm not trying to discourage you, but perhaps you might want to start with a more basic problem to learn first? My understanding from your post is that you don't have a good grasp of basic electronics - this isn't a problem, because everyone must start somewhere, but laser diodes are notoriously unforgiving for mistakes.
Ok, so here's a few pointers to help you get started. You didn't indicate what your ultimate goal is, so I can't comment on whether what your doing will accomplish it. When working with diode lasers, be very careful as ESD (electro-static discharge) can permanently damage them. Always ground yourself (use a grounding strap, or keep in contact with a metal desk or something like that). Secondly, you might consider placing a LED in place of the laser diode in order to test your circuit first. The LEDs are much more forgiving and that will allow you test things first.
From the Sparkfun laser you linked to, it appears that is a prepackaged unit that you give a "2.5V to 4.5V input voltage" in order to power it. The potentiometer on the laser will control how much current it draws, but any pin on your Arduino will not be able to source that much power. It also appears that that unit does not make it easy for you to cut it on and off via a I/O pin on the Arduino. If you want to be able to control the light via a I/O pin, you'll need something more like this: http://www.sparkfun.com/products/8654
A few comments about your circuit questions:
If you hooked the laser directly to the 5V pin, when the laser is only rated up to 4.5v, that's a likely cause for why it burned up. Perhaps if you described exactly what you want to do, and drew a picture of what you tried, you'd get better help?
Self-test pin: Going by the description page of your breakout board, seems this pin would already be connected to a pull-down resistor, which thus disables the self-test feature. You don't need to change anything here.
Power-down pin: Must be driven to GND for the LPR550AL to operate. So put a solder-short or a wire between the Power-down pin and the Ground pin next to it. But alternatively, if for some reason, you want to use this pin to trigger the LPR550AL's Power-On versus Low-Power state on the fly, you can connect it to an Arduino pin (in your code, be sure to enable the internal pull-up, then write a LOW on it for LPR550AL Power-On operation).
Low-pass filters on outputs are for noise reduction. Your board, as designed, seems to already have them, so the board is ready to go. This is clearly described on the page that you listed in your question; please read such details on your original breakout board product page as well as the datasheet of LPR550AL before asking these questions!
VIN is your non-regulated input, and VDD is the regulated 3.3V that also powers the LPR550AL on the board.
Circuit: If, for whatever reason, you need a reference for setting up your own circuit (instead of using the breakout board), you can refer to this circuit diagram for the same board (source: bottom of [this Pololu webpage](http://www.pololu.com/catalog/product/1266 )). The circuit doesn't look too difficult, and the suggested capacitor and resistor values are fairly common ones.
Best Answer
Connecting anything much above 3.3V (as in say 3.6V) to that rail would fry the Arduino. A transformer only operates with AC voltage not DC, so the best way for what you want to achieve is a step-down regulator also known as a buck converter. Variable ones that can accept 24V DC and output 3.3V (be careful to adjust it before connecting) are available on e-bay. Here's the first example I found:
DC Adjustable Voltage Buck Converter 4.5-25.5V to 3-24V Step-down Power Module
But important: I'd taken at face value that your statement was correct that it was OK to power the board from 3.3V over that line. As Peter Bennet correctly states some parts are actually 5V based and the 3.3V rail is the output of a regulator. Without removing the regulator and knowing the exact consequences that isn't a good idea.
Instead you should consider setting the regulator for say 8V and connect it to the 6V-20V input socket on the Arduino where you'd normally apply an external power supply / wall wart etc. That gives you a bit of extra safety if the adjustment on the regulator ever gets changed or drifts a bit.