If the visitors are clicking from your site to the merchant, it's fairly simple. All you have to do is add a unique url variable to the CJ link:
If this is an example aff link:
then it would become:
where the 123456789 is unique to a particular visitor (up to 64 chars I think), so you can't just hard code it into your aff links. Best to use some scripting such as coldfusion, php, etc.
In coldfusion, it would look like this:
where #cfid# places a number that is unique to each visitor on the end of the url if you have enabled application variables. Alternatively, if you don't have server-side scripting capability, then you could send your clicks through another tracking service that would simply tack it on for you before forwarding them to the CJ network.