These instructions are based on VOGUE PATTERN No. 8426, published c1943.
There are only two pattern pieces (well, the pattern does include one for the hat band, but since that's made of grosgrain ribbon, it seems redundant). The top of the hat, as you can see, is slightly oval shaped, and measures 7 1/4" by 6 1/2". The side piece is about 19" long. There's a 1/2" seam allowance on these.
Cut one of each piece out of your chosen fabric, a stiff interlining fabric (the pattern calls for buckram; I used a stiff felt-like pelmet interlining, which is very easy to work with), and lining fabric (I actually dispensed with lining the hat since no-one's going to see the inside).