Using the pattern above from Happy Together, first you cut out your curved headband piece and the straight piece for the back of the headband. You can use the same fabric, or contrasting fabric, or two completely random fabrics. You need two headband pieces and two backing pieces.
Sew the long edges together, leaving the short sides open. Sew this way <------> on the picture below.
After this step you can iron. I found it useful to press the piece to make the edges crisp, especially because I was using two different fabrics and didn't want the edges to roll.
Once one end of elastic is anchored, finish threading the elastic through. Scrunch the backing together and close the other end of the backing piece, anchoring the elastic in place.