If you want a contest that can really make your book go viral and bring you a lot of attention, and you already have an existing audience through an email list or facebook fanpage or website, then here's an idea…the original question was asked for somebody offering a cookbook so it's tailored for that market, but you can adjust it easily to work with your book's market:
- Lower the price on Amazon (or whichever channel you want to spur sales for) and let folks know that that price is only available during the contest. (I recommend Amazon because they're the gorilla and price changes usually get reflected reasonably quickly – often within 12-24 hours or less.)
- Provide a place where folks can get a sample PDF with a few of the recipes.
- Create a YouTube video about the contest, with this offer:
- Make one of the recipes from the sampler PDF (no purchase necessary!) or use a recipe from the book (on sale now until the contest ends!)
- Mention the contest entry requirements, which could be one of the following:
- Record a video describing what they thought of the process of preparing the meal (how difficult, how much time?) and what they thought of it (how tasty? did the family like it?) Bonus points for including video of preparing or consuming the video, but can be as simple as using the built-in tools to record the video using your webcam and the YouTube website. Enter it as a video response to the contest video.
- Take a picture of the dish after preparing it and post it to facebook and/or twitter, bonus points for including folks eating it!
- Write a comment on the contest page with their experience. Bonus points if you link to a video or image.
- How entries are judged…random selection, popular vote through likes/retweets/a poll/etc, or panel of judges (could be just you.)
- What the prize will be.
- Send traffic to the contest, and try to tie in a viral component to it. There are services that will help do that, but you could just do it by sharing the page with your email list and fanpage base.
I wouldn't recommend having more than one way to “enter” the contest unless you are doing something simple such as a random ballot for liking/sharing/commenting. The higher the barrier to entry, the fewer responses you'll get, but the more engaged your contest entrants will be. A comment/like/share/retweet is much simpler for a user than a photo or video. However, a suitably awesome prize can justify the tougher barrier to entry, and if you include some sort of viral component in the judging then it can really help a contest spread (even by people not taking part.)
For example, you might have people share their entry to get your pool of finalists, and then do another popularity vote based on just those or do a panel of judges at that point. You could have a really cool prize for the winner(s) that actually enter, and depending on whether you can track it or not you could have smaller prizes such as copies of the book for folks that interact by commenting or sharing.
It can be some work, but if you have a large enough audience to seed the contest with and can make the contest go viral it can lead to a lot of sales and attention.
Also note that this particular idea probably would work best with a mass market niche, and may not work as well for your UBC. But, it can be an additional (high-price!) service that you can offer to people as an upsell…