To make the hat's main section, cut out a rectangular strip out of cardstock or construction paper with the following dimensions:
Length - must be long enough to go around the doll or figure's head. Add an extra ½" or so for gluing the edges. My strip is 6½" long.
Width - defines how tall the hat will be. Add an extra ½" to ¾" for gluing the brim and the top piece. My strip is 2" wide, the resulting hat will be around 1½" tall.
Bring the end with glue over the opposite end to come up with a cylindrical piece. This piece is called the top hat's crown. To make sure the hat will be a perfect fit on your doll, place the crown's opening on your doll's head and adjust the overlap as needed.
Once happy with the fit, press on the seams to glue in place.
If you want a perfect circle, you will need a ruler and a compass. First measure the diameter of the crown's base with a ruler (e.g. mine is 1.8"). Next, set the distance from the point of your compass to the pencil's lead at half the measured diameter (e.g. If the diameter of the crown is 1.8", the distance must be 0.9"). Turn the compass to draw a perfect circle.