Whenever two people have a graphic battle, they are basically making images and competing to see who did a better job of making any random kind of graphics.
The way they are started is someone requests a graphic battle in a post, two people want to do a graphic battle, or someone calls someone or anyone out.
Once the people created a guideline as to what the image should look like (theme, colors, and other requirements) they create a due-date for the images to be done by. Once they both have images up, they post a new poll and users vote for the best one. You can make a vote limit so the winner will be decided when there's enough votes!
Did I miss anything?