So, what is contra dance and where does it come from?
Contra dancing has a very long history in both Europe and the United States. In fact, it predates the existence of the United States! Many of the signers of the Declaration of Independence undoubtedly were contra dancers. The contra dance that we know is only one type of "contra" dance. There are culturally specific forms that are danced in Brittany, elsewhere in France, and in the Caribbean!
There are a few conventions that seem to be common to dances in the United States. We wear clean, soft-soled shoes so that we don't slip and slide around or mar the dance floor. (We love our dance floors!) Before almost every dance, there will be a half-hour "new dancer workshop" to introduce new dancers to the figures that will make up the evening's dances. It is the custom that anyone can ask anyone to dance. This is great for new dancers, because it means that you can take the initiative to ask a more experienced dancer to dance. (This will help you to learn and feel comfortable during the dance.)
A lot of folks are kind of shy until they get to know people. One of the nice things about contra dancing is that, since you and your partner dance with different couples each time through each dance, you will interact a lot of people in passing without having to think of things to say. Almost all dances have a break about half way through the evening, and in Michigan we'll have snacks. This provides a nice low-pressure opportunity to chat with the folks with whom you've been dancing to get to know them better, if you want to.
There is a reasonably good general description and history of contra dancing on Wikipedia.
tFor you folks who just want to get right to it, there are a couple of links to videos lower down on this page on "Contra Dance Basics", "A Short History of Contra Dance", European quadrille, Breton country dancing, Basque country dancing, and Caribbean quadrille.