How to use Garmin's battery more effectively?
From my research, the Garmin Edge 800 uses a 1Ah lithium ion battery. 

In general, these do not have a memory effect like older rechargeable batteries. But some care is still worthwhile, for example storing the battery completely charged (in a hot environment) or completely discharged is damaging. 

Partial discharge cycles are generally seen as good for them. A full discharge and recharge every 30 uses is recommended by some sites.