The yarn used in the picture is Bartlett Yarn's Acadian Tweed 2-ply, but any worsted weight yarn will do.
#9 needles, short length Tapestry Needle
The garter stitch is used.. you just knit every row.
Gauge & Size:
The gauge is not important and is not worth troubling a young knitter with if this is their first project. Any size is right! ...although the purse won't end up being too large since there are not that many stitches. The important thing is, that the child be able to finish the project and feel good about what they have accomplished.
Knitting the Purse:
Cast On 18 stitches. Knit every row until the piece measures 8 inches. Change the yarn if you wish the flap to be a different color. Knit 6 rows. Decrease 1 stitch each side every other row until there are 10 stitches. On the next row make a 2 stitch buttonhole in the center. Continue to decrease 2 stitches each side until there are only 2 stitches left, then bind off the last 2 stitches.
With the tapestry needle, sew up both sides of the purse. Sew on a button.