First, you need a basic invite (I seriously use free clip art from the internet for this) to explain the details - date, time, location of course - and then an RSVP for people who want to bring a chili so you can have the right amount of supplies ready. I always note that for anyone NOT entering a chili in the contest, they can still bring a chili-related side (cornbread muffins, cheese/sour cream/cilantro, beer bread, etc) and can still join in on the sampling fun! I also request the chili to be dropped off at my place sometime before the party so that I can have all the crockpots ready to go and I can have the sampling already lined up to start the party!
So the idea here is simple - no one knows which chili belongs to which guest (hence having them all set up ahead of time) so it really is a fun blind vote. Everyone samples each chili and then they get to vote on their favorite. I also had some other finger foods available for people (like the kiddos) who may not be able to handle all the chili - I made pigs in a blanket, chicken quesadillas, etc. I had some "voting rules" made up stating that you have to actually EAT the chili though to be able to vote - that way hoards of kids aren't voting for something they aren't even participating in. :)