As a moderator, you need to be especially weary of promoting the site that you're moderating. Moderation is a strong affiliation, and promotion from you is likely to be considered spam in many online communities. It's often better to leave the promotion to ordinary participants.
Some online communities allow users to have a signature or profile where they can pretty much advertise whatever they want. In these communities, put a link to the site you want to promote, and add a very short tagline that will appeal to your readers. Often, even if the site you're promoting has an official tagline, you'll want to use a different one that's targeted to your audience.
Beyond this, tread carefully. Many communities have rules regarding promotion; make sure that you follow them in letter and spirit. Don't get into technicalities regarding the rules: if it gets to that point, you've lost.
Typically, the more established a user you are, the more you can get away with. If you're new, don't spontaneously mention your site: wait for a directly relevant topic to come up. After a while, the occasional spontaneous mention of a new, interesting item on your site might become ok. Don't participate only to mention your site: be a member of the community in good standing, and people will listen to you. Don't be this guy who keeps harping on about his site, be this guy that everybody respects, and hey I should check out his site, it must be good if he's on it.