Inspired by the past with a little bit of modern flare!
For the cardboard definately make sure it is light and flexible. I used a cheez-it box :-)! But you could defiantely use something like a cereal box or pop-tarts or whatever. You don't need alot so no worries if it is a smaller box.
Take a couple strips of packing tape and wind the strip of cardboard around the circle and tape it down.
cover all the outside edges with tape as well as the spot where the two pieces connect on the inside to keep the shape secure and the pieces together.
don't worry if it looks sort of crappy because you are going to cover it with fabric anyway.