Some of the best ways to attract new page followers:
Use Invite Friends feature,
Use Import Contacts feature and invite current clients/subscribers,
Add the Facebook Page Plugin (Like Box) to your website,
Polish your Facebook page: set up the vanity URL, update the cover photo and profile picture for a good first impression, and make sure the page settings are correct,
Engage with other pages as a page: this will give you additional exposure to their audiences,
Do online cross-promotion: utilise all the other online channels that you have access to, such as other social networks, email campaigns, video sites,
Use offline promotion: include a link to your Facebook page on any merchandise, flyers, posters, business cards, menus or any other offline promotional material,
Develop a great communication strategy: start by defining the audience, what are their problems and needs, and offer the solutions to those problems with your content,
Engage your fans: at the very least - ask questions, also reply to every single comment and message to build a stronger personal relationship with them,