using android to power a PIC board
To answer your question. Your battery want to see a "constant current"
This is a very good example of how charging current should evolves with battery voltage. It depends on your battery ratings...


Some reading about Lithium battery charging can be found here.

Search for battery charger IC from diferent manufacturers (for Linear here).

The good news are that your mobile phone already incorporates a Battery charger IC, so apply 5V to the USB charging connector and you will be charging your battery.