Start out with a large sheet of black construction paper (e.g. 24" x 36"). Create a large cone following this basic cone hat instructions. Make sure that the base of the cone fits comfortably around your head, with a bit of extra room for adding a brim.
In order to fit both the cone and brim in a sheet of 24" x 36" construction paper, draw the semi-circle when making your cone as close to the sheet's edges as possible. This should leave enough construction paper to create the brim later.