The simplest contest to hold would be "enter to win!" This kind of contest has the advantage of having a low barrier to entry. I've done it before, and I got an overwhelming response.
The other time I ran a contest, it was for a kindle ebook version of Spinner Of Lies, and I asked contest entrants to "spin me their best lie" on their social network to enter. The number of entries fell by an order of magnitude.
So.... I wonder which is better, or if there's a better middle ground, a contest that requires fewer hoops? Putting on my thinking cap, but if you have a suggestion, I'd love to hear it!