Use Giveaways and Organize Contests

You can organize a contest on your Facebook fan page and give something away for free to your readers.

This will help you in getting more followers because the people that already like your page are going to invite their friends as well to take part in your contest.

You can add a rule that all the participants must like your page in order to be eligible to win the prize. Here’s an article that explains how you can run a Facebook contest successfully and check out this post to know more about contest ideas to get more likes.