How do I re-charge the C200 battery?

I have both C240 & C250 players so I shall assume that your C200 uses the same method:
there is the cable included with the C240 player that has a USB connector that goes from the PC or laptop USB port to the player's multi-pin connector. This supplies power to the player to charge the battery. When you plug in the cable to both ports, the player's display will light up and you will see a little "battery" icon symbol in the upper right corner of the display that indicates the charging action and status. It's tiny and hard to see, but the green on the battery icon will get a steady green color when charging is complete.
Also, after-market re-sellers (Dealextreme, et al) have both car outlet and house wall outlet adapters specific for this model, as well as generic models with USB ports. However, I cannot vouch for the safety or quality of these merchants or their products.