The physical forms can be anything that will hold up the brick. The traditional method was to build a form of wet sand, which would be shoveled out afterword. The most common here is ribs of foam insulation that can easily break out when your dome is done. A couple of recent builders used a
hinged swivel arm (My indispensible tool (a variation on a FB theme)) invented by Jim (jcg31) to place each brick: This works best with the hemispherical oven.
Some builders build freehand. It all depends what you're comfortable with.