I find that the best method to promote your site on Facebook is to take the unconventional approach:
Promote your Facebook page on your site! Add "like" and the direct link to your Facebook page on your site and you will get followers over time. Once you have followers, your social media exposure will flourish. The trick is to get a few followers and the rest will follow.
I am using both Facebook and twitter to get the traffic for my site .I have analyzed that Facebook gives quick results than twitter.You can join face book groups according to your niche.You can also create a face book page and you can promote it and get traffic.
So i suggest you that first off all you have to make followers than you can get better results from social media sites.
I use plugins that autopublish my blog posts to my FB fanpage's wall and my Twitter feed. This is a good first step but you need to make sure you have a large FB fan / Twitter follower base. You can boost your numbers of TARGET readers by finding blogs in your niche that use Facebook for comments. Post using your fan page identity. For twitter, use the hashtag feature when tweeting about your tweets.