A simplistic option available would be one of the common portable charger packs that are advertised as a means to have additional talk time on a telephone. The output is typically low current, anywhere from 0.5a up to a couple amps, perfect for these gadgets. The output connector is usually USB mini or USB standard A type, unless you mistakenly buy an iPhone specific device.
A quick check on a discount web site finds this:
http://www.rakuten.com/prod/2600mah-uni ... 91179.html
There are many other options in that line of product, depending on your duration requirements and size restrictions. If you were to run with an ordinary battery option, you'd want one with a five volt regulator as part of the circuit. LiPo batteries are 3.7v per cell, running to 4.2v on a full charge. One is possibly too little voltage (I'm guessing here) while two is too much voltage, but perfect for a 7805 voltage regulator.
I'm not an engineer and I don't play one on television. My method of building things is to try something. If it burns, breaks or explode, I don't try that method again.