Running a social media contest?

[canphoto]

I'd like to run a social media contest where I ask people to mention my WordPress site (running Genesis and Copyblogger template) on Twitter and/or Facebook. I have two donated books to give away as prizes, but I have no idea how to track the participation in something like this or how to pick a random winner.

I've been searching for a day or two and have found a couple paid services that seem like they might do what I want, but I'd like find a free way to do it if I can. My site's small and doesn't generate much income now.

Any suggestions would be much appreciated.

Thanks.