The CBR600 battery is under the seat. To get to it, lift the rear
corners of the seat slightly to show the allen head bolts that hold
it on. Carefully undo these to release the seat and reveal the battery.

If you are having continuing problems with it it is likely it is old and needs replacing, you'll need to fork out around £40-50 ($65-80) [2013 prices]. As always you get what you pay for, find a good one and shop around for a good price.

There have been problems with the Honda charging system so if you continue to have problems have the bike checked by a garage.