Polymer Lithium Ion Battery - 3.7V 2400mAh (CE04379)

Hi Andrew
Just butting in here with my two bobs worth.
You can’t use the 3V3 regulator as linked by Samuel straight from a 3.7V cell. The typical drop out voltage at 500mA is 1.05V which for a 3.3v output you will need a minimum input voltage of 4.35V. As that cell has a nominal voltage of 3.7V it is not enough. I think what Samuel had in mind was to convert 3.7V to 5V with a step up converter then use the linear regulator to get your 3.3V. This should get a very clean 3.3V as the linear regulator will get rid of any switching ripple left on the 5V by the converter. A little wasteful on power but is the only way you are going to use a 3.7V cell to get 3.3V.
If you started out with a 5V power supply it would be better but I think you want to use battery.

Cheers Bob