One method that is probably the most effective -- and fastest -- way of increasing Facebook Fans is to advertise your page on FB. If you create an ad that achieves a high click through rate (>.5%) and you get social sign ups (other people decide to Like your page because they saw a friend do the same), you can get fans for pennies apiece.
Facebook ads are still wildly underutilized in my opinion, and have some very cool targeting features you can't find in Adwords. I.e. you can target by age, city, gender, relationship status and keywords that appear in the profile. The downside of course is these are "display" ads, meaning people aren't searching for the information you are advertising, so depending on the product or service, it can be challenging to find the combination of ad creative and copy that does well.