That's an interesting question coming from somebody who has earlier claimed to have suggested several sites
But never mind, I'll give it a serious answer. Take some time to find the one most relevant category for the site. Click "Suggest URL" at the top of the category page. Fill out the form, and pay attention to the instructions. Send it in. Check to see that you got a "Thanks for your site suggestion" screen (that's the only confirmation you get of the suggestion being successful). Do this only once, unless the site has relevancy for both a topical and a regional category (a sports team will typically be listed both in the category for the sport and the category for their home town, for instance.)
After you've sent in the site suggestion, there is nothing more you can do to make the review happen sooner. There are ways of making the process take longer, such as suggesting the site many times to a range of related categories.