Hi James,
When you "submit" a site to dmoz.org, what you are actually doing is submitting a suggestion that one of the editors review the site and list it. The review might happen within a few days after your suggesting the site, or it can take several months or years. There is no way of knowing (even for the editors), and no time frame when a specific site has to be reviewed.
This site is not the same as dmoz.org, it is an unofficial forum which is run by a few of the editors at dmoz.org. You cannot suggest sites for review here. You also can't log in to the editor-only areas at dmoz.org unless you are an editor there; to become an editor you need to apply through the application form on that site, but unfortunately that is not possible at present.
There is plenty more information in the FAQ here at the Resource-Zone -- it's linked from the top of each page.