Li+ / LiPoly batteries should be charged in a constant current/constant voltage scheme.
At initial charge, a constant current should be used, until the cell reaches 4.2V. At this point, the charger should charge at constant voltage until a threshold current is reached.
The current to charge with varies with battery. The C rate is usually good. If the battery is 4.1Wh, then it's about 1Ah. 1A constant current until 4.2V, and charge cutoff at 100mA would be a decent solution.
It is very important to *not* let the cell be charged above 4.2V, unless you want some interesting pyrotechnics.
See the
Cheers
PeteS