How do I promote my FB page without paying?

You can log in under your page name so any group posts or comments you make link back to the site. Of course creating quality original content and not just sales pitches helps to attract a following.

You can't capture people from those other sites unless you paid to get ads placed there.

Do consider using Facebook paid ads at least for a short term likes seeding campaign to get the ball rolling.

I think one of the best ways in increasing likes in Facebook is by having quality contents shared to social networks. You can also use tools like http://postific.com/