On Facebook, I've found the best way to get fans that are not already connected to you (on your personal FB account - and most of them don't matter because they probably like your page because they like you more than they like your page) is to find other larger pages from related groups and organizations, add photos or content to those other pages. People who like those related pages will then like your page. It's slow, it takes some work and you need to find the proper balance of adding content that people find useful without filling up other pages with stuff that might be considered too much and therefore spam.
When done this way the people that like your page tend to actually like it and very few unlike it. Adding FB icons on the actual website so people can like a page or a post from the site itself results in a few likes of specific content and even fewer likes of the Facebook page but it doesn't hurt to add it.