To use a callback function you need to specify the GET parameter "json.callback" in the URL to the REST robot. For example you would have a URL like this:

http://service.openkapow.com/...?resultformat=json&json.callbackFunction=myVeryOwnCallbackFunction&...

Then you of course need to define the javascript funciton myVeryOwnCallbackFunction that takes one input parameter. This input parameter will be the JSON output from the REST robot.

 I hope that clarifies things a bit!