This really is a piece of cake!
Tools required: Philips-head screwdriver, common sense.
Materials required: 12V 7AH (12 volt, 7 amp-hour) sealed lead-acid cell. Widely available from around £15, such as the Yuasa NP7-12.
The hardest part is removing the battery pack from the fabric holder. It is fixed tightly with velcro, but once you've got part this, it just slides out.
Lift the battery out of the plastic bucket it sits in.
You then need to remove 12 screws - five on either side and two on the bottom.