Can you only promote it on your own website and mailing lists? I thought it was like CPA stuff.

Some clue of where to start please, are these guys CPA and can you only do it with your own website?

CJ is about affiliate marketing. Which means you put links on your site and if someone buys something after clicking your link, you earn a comission.

Your next step would be to find relevant programs. You have to submit your application for each program you want to promote. If they accept you, you can grab the links and start earning money.

I suggest you to read more about CJ in the forums here. You'll find a lot of useful information.