One of the complaints some folks had about Facebook Pages was you couldn’t invite anyone to be your “fan” (the business term for friend).
However, now you can post your Page (business) to your Profile (personal) and/or invite specific friends to come check out your Page and Become a Fan.
Go to your Facebook Page, and click on the Share with Friends link at the top right.
You can Post to Profile (that’s your personal profile) which goes into your Mini Feed and pushes out into your Friends’ News Feeds.
Or, the default is Send a Message where you can insert Friend names, Friend Lists, and/or for those contacts not yet on Facebook just type in their email address.
Be careful not to overdo the inviting though. Facebook frowns upon heavy messaging and you could receive a warning. I recommend just inviting a few people at a time over several days or even weeks.