Replay,
You would set up a competition in a way that encourages people to share or like a page. For example you might fangate your page and have a form that people have to fill out. Make it so the only way they can get to the form is by liking the page.
You can entice people to share content by saying they will be entered to win something if they share a post. That way people who are interested in what you are offering will share the post . Those are just some basic ideas.
Hope that helps,
Shawn