Work for a site that does a lot of those contest "thangs" and here are a few issues. First, make sure you have legal issues on what constitutes valid entry figured out (will you accept entries from outside the U.S.? Give exact closing time in GMT or specified time/day! Are they submitting logos, blurbs or other "content" that will become yours/sponsors'?). You should have the entire contest terms figured out at the start.
From here, YMMV depending upon what kind of contest you're envisioning. I highly recommend auto-emailing the entrant a confirmation of their entry. This really cuts down on the queries you'll field from contestants.
I've handled a few of them... mostly quizzes. I set up the entry forms so each answer returned a different subject for the entry email, and set up filters for the incoming mail. That way, everyone with an incorrect answer was filtered out automatically. Then I counted the number of correct emails, turned around, and asked someone random in the office to give me a number between 1 & X (however many right answers there were). I'd count that number down from the top, and there was the winner. Paperless random drawing.
Had the terms & conditions right on the entry page, between the bottom of the form and the submit button... everyone had to at least scroll blindly past them to enter. ;) (How many licensing agreements did you actually read *before* you installed the software?)