You first need to begin with the wagon box which is also known as a Yankee bed. This bed consists of wooden planks or boards. You need to set up a large board which will be used as the bottom. It should be somewhere around 10 to 12 feet in length and 4 feet in width. Now on the bottom planks you need to bolt two more planks which need to be 10 to 12 feet in length. You can use tar and caulking to fill the gaps in the boards.
You now need to select a beam of the same length as the Yankee bed, which will enable you to provide support to the wheels. The important thing is that it should be big enough to cover all your passengers and strong enough to support the weight. You now require four foot long beams and bolt them to the end of the main beam. Bolt them in such a way that they are perpendicular to the beam. The four foot beams should also have a brace on the underside.
An axle needs to be passed through the braces. Get a wagon wheel and attach it to the end of the axle. A wagon wheel has wooden rims, wooden spokes and the rim has to be enclosed with an iron tire. It is recommended that instead of trying to build your own wagon wheel, you buy one.
You now need to make the bows with the thin beams. These bows go at the top of the Yankee bed. You can make the beams by steaming and then slowly bending them. Remember do not bend them quickly, as they might break. These bows now need to be attached on the sides of the Yankee bed. Space these four to five bows evenly. For the cover, just stretch a large canvas over the bows.