For this style of closure, you will need two buttons and some thin elastic cord.
Tie a loop with the elastic and secure the knot with glue.
Place one button on top of the knot of the elastic on the top "lid" of the bag, with the loop pointing toward the edge. This button isn't necessary, but it covers the knot and looks pretty. Stitch the button to the bag, stitching to either side and in between the loop ends (just below the knot). This should secure the elastic as well as the button.
Stitch the other button on the other side of the bag opening.