no not a zero cost, but i can help you to get millions of fans @ 100$ only PM me if you are interested.
1stly if its new fanpage,just buy from anyone that can gve u like as a startoff,recommend go to fiverr.com... a new fb page that doesnt hve like will lessly be liked by real people... even u get fake like but if u have 400-500 as startoff,its not prblm... After u hve some likes,try to start off by post a usefull post instead of directly promote your site/products/services... to be continue...too long...
Make sure you have a 'Like Us on Facebook' button on your site - it's free to do. If you have a Twitter, tweet that people can also 'like' you o Facebook. Basically suggest it anywhere it makes sense to. Could be worth adding to footer of emails for example.
Yeas, there is a way, but it takes much time.You need to promote your page and to hope to get likes.Or buy them...
Free method, start with your current lists, get your friends and friends of your friends to all like you and keep passing it on..GO VIRAL! Or offer something for free for visitors who become fans.
Maybe this article can help you : http://news.yahoo.com/not-just-another-button-chat-virtual-person-converts-094220669.html