Has your site been indexed by Google, i.e if you put in 'site:yoursite.com' into Google does your website come up? I think Google CSE just allows you to use the Google Index and to specify which sites it should search. Therefore if your site has not been indexed by Google then CSE will not bring up any results. If your site is new you will just have to wait untill it has been indexed (likely to take several weeks) and then CSE should work.
I have it working on our site here:
http://1stoultonbroadseascouts.org/search.aspx
Although it works I'm not currently using it as 1. the site isn't currently big enough to need it and 2. it doesn't always bring up the most applicable results (and there is no way to directly control this). There is no point having something just for the sake of it, it has to work well and add value to the site.
I hope this helps.
1st Oulton Broad Sea Scout Group Administrator