The long needle is called a circular needle, you can knit flat with it, just like with straight needles. It's good to knit tubes in the round like hats or mitts or sweaters, and generally you would use one slightly smaller than your item, or you need to use the magic loop technique. Knitting in the round is shown on the Advanced Techniques page.
You can use the purl video to learn how to do that, just be aware that if you purl every row, you get garter stitch the same as if you knit every row. To get stockinette stitch, what most people think of as a knit fabric, you have to knit one row, purl one row and alternate them. You can practice that, along with the Increases and Decreases.
Get some inexpensive yarn if you don't have any leftovers and just practice. Cast on about 24 stitches, do a couple knit rows, then alternate with the purl rows. Do decreases then increases. Practice ribbing which is combining knits and purls on the same row - k3, p3 or k2, p2, or even k3, p1. Just play around with the yarn and needles and see what you can get them to do.