Depends on the topic relating to your site, meaning what is your demographic, if its about Naruto, DBZ, Bleach or General Anime. You will want to get backlinks from other sites like your own. Also try to place a link back to your site in your forum signature on the various forums you visit and ask friends to do it as well. Using google advertising and others like it should be avoided unless your a company otherwise just take the fansite path I have layed out.
Go to anime forums and let them discretely know about your site but don't spam. Submitting to as many social bookmarking as you can will also help you with your promotion.
Promoting and Advertising techniques are almost the same for any site at least at the start. Reach you audience, work on your keywords and try to dominate in SERPs