How to use a smartphone / tablet battery?
This is a typical Li-Po battery singe cell. Two Black wires are ground, two Red wires are positive terminal. 

Green wire is related to battery temperature sensor, and the next White wire is battery ID (some serial format).

For DIY purposes you can simply charge the cell as usual for Li-Ion cells and ignore ID and temperature sensor wires. From my experience with this line of ASUS products, the safe charging current for this cell would be ~2A, and the terminal voltage 4.2V for full charging capacity. Or even higher. At least my MemoPad ME851 has similar battery with no-load voltage that reads at 4.293V fully charged.