Much of what's being suggested here is pretty far off.
First off, NEVER try to charge a li-ion/li-polymer batt manually. The charging algorithm is very specific, generally it is a fixed voltage (current limited though) until the current drops below a particular threshold for that cell type and then the power MUST be cut off. It's also more complicated for series cells. Failure to shut off at the right time will overcharge the cells. Lithium technologies are very sensitive to overcharge relative to any other rechargeable. At best, this will permanently damage these particularly expensive cells. At worst, it will catch fire- this is not hard at all to do with li-ion.
Now back to this comment on longevity. Li-ion should never be run totally dead (near 0v), but no "proper" device will do this. They will shut off when the voltage drops below a specified threshold and this is what your camcorder calls "dead".
Storage. Li-ion/li-po are actually degraded by time left at full charge, completely opposite from lead-acid. Calendar lifespan is dramatically increased by storing at like 1/2 charge or less. Unlike lead-acid, the number of complete deep cycles doesn't have much effect on its lifespan. The time spent with a full charge, or near to it, is the big factor.
There are some who maintain that a particular battery type's performance can be improved by conditioning it early on. In some cases this may be true, but if so it's not a really significant effect you should concern yourself with. Just go by mfg's instructions.