Basically you and I would pick one of our characters for the other person to draw, or we could draw two of our characters together. That is what a typical art trade is. And you usually agree upon a time frame to finish the art trade in, like a few weeks to a month. Its pretty casual and pretty fun.
Its always good to make sure both people have time to complete the trade, or you may be waiting for months.... I'm still waiting on one I did in the spring.