Simple stand-alone power supply for an arduino device?
Here is a possible DIY solution for solar powered Arduino system:
https://www.cooking-hacks.com/documentation/tutorials/arduino-solar/

The principle is pretty basic. A rechargable battery sufficient to power the system for 18-24 hours, a panel of photo-voltaic cells (solar battery), and something to manage charging the battery from the solar panel.

There are many possible solutions, from full custom assembled from various parts, to a turn-key complete system in a box.  It would be good to have a basic meter if you are playing around with electronic stuff.  You could measure the actual current used by your Arduino, and calculate the size of battery you need for the expected solar radiation in your location. You would need a larger battery farther toward the polar regions than you would need near the equator, etc.