The easiest thing to do would be to add another battery and use it as is, 24 volts. The second easiest thing is to scrounge an old 12 volt starter and use that.
The hardest thing to do is rewind the original to use 12 volts. To get the same amount of power into 1/2 the volts, you'll need to increase the diameter of the wire by at least 2x. Given the amount of space existing in the laminations, you'll more than likely have to decrease the number of wraps per coil by the same amount or more. While this should give you the ability to push a lot more amps (and thus the same number of watts at 1/2 the voltage) It may slow the speed of the motor to where it's unuseable. Depending on the way the 24 volt motor is made, you may be able to pull 1/2 the magnets/brushes and rewind to suit the new configuration to keep a decent speed. It's a pain and takes forever. However, if you like that sort of thing ...
You can see my web page(s) to see how I did this the other way around (rewinding a 12 volt motor for 24 volt generating).
http://www.greeleynet.com/~cmorrison
