You must figure out what you are going to gain from a Facebook contest. The contest must be aligned with you marketing goals which means it must be a planned and strategic component of your marketing campaign. It seems like an obvious thing to say, but you have to know your target market. If you do not serve a wide range of people then it is probably best you find another way to give them rewards such as prices.
Next, figure out what kind of results you want to drive from such a contest. Do you want an increase of “likes” on your Facebook page? Do you want to drive customers into your stores? Increase sales? Perhaps simply build brand awareness? The point is to set a goal and achieve it through this contest.
There are four types of contests: photo, video, essay, sweepstakes. You have to decide what will work best for your audience. If you are a company that can easily engage with the target audience, try a photo or video campaign. Doritos ran a contest that allowed people to upload their version of a superbowl commercial for the company. Take a look at some one the finalists here: http://youtu.be/HY4L1ihRkaY
For any successful contest you must have mobile capabilities, embedded content so that you can put the contest on a variety of online platforms, and a relevant prize. Depending on the amount of effort that contestants are required to put into it, the prize must reflect what they have done.
Lastly, get the word out there! Advertise. You have to promote your contest on not only all of your online platforms including all social media outlets but also find meaningful inbound links which can make all the difference.
Once all is said and done, monitor your results which will not only help you to determine if you achieved your previously set goals but also will help you figure out what to adapt for the next contest.