First I must retract and tell you all that running a Facebook giveaway on your page is not allowed. Many people do it and will get away with it but you can get your page shut down if someone reports you. So it's best to use a 3rd Party Application for your giveaway. Some of these you can add to your Facebook page as an extra tab so people never have to leave Facebook to enter.
Here are some giveaway apps designed for Facebook that you can check out. I use the Rafflecopter free plan but plan to check out some of the others. If you know of others or have experience with any on this list please give us your feedback in the comments section on this post.
1. Rafflecopter http://www.rafflecopter.com/ free for a standard giveaway, add photos and other social media options for a monthly fee of about $60
2. Woobox http://woobox.com/ they have a few options for free like adding social media tabs and have a try it for free option for their several giveaway/sweepstakes/coupon apps. After the free trial it is $15/month for up to 1000 fans $29/mo for up to 20,000 fans and then have a sliding pricing scale as your fan base grows past 20,000
3. Offerpop http://www.offerpop.com/ A bit more pricy but touts the the names of customers such as Ann Taylor, Toms, Forever21, and Vogue. They offer much more than just giveaway apps so if you are an established line with a healthy marketing budget, check them out!
Now I absolutely love the Momprenuer Blog so rather than reiterate the info I am going to direct you to her page to read the most detailed but most understandable post on holding a giveaway. It covers everything from what is legal, who you can offer your giveaway to without violating federal laws, what you need to disclose when you post your giveaway, and how to announce your winner.
Here is the link. Be sure to comment on her post that the Fashion Business Mentor sent you. :) http://businessamongmoms.com/blog/2012/05/23/mompreneurs-guide-operating-giveaways-conteststhe-right-way/