Last week I taught the same technique to a group of adults at the public library. It takes a bit of finessing to get a coiled basket started, but once you get to about the third row, it is really easy, and something you can work on while watching tv, or with your crafting group, etc.
Here is a photo of the four coiled basket samples I made for the class.
For these baskets I used cotton clothesline from the hardware store and inexpensive yarn (acrylic) found at fabric and craft stores. The largest basket, 1 1/2" tall x 4 1/2" across at the top, used 10 feet of clothesline and about 30 - 40 yards of yarn. I used a #18 tapestry needle (DMC) to make the stitches.
These little baskets are quite firm. I take a stitch after about five wraps, always pulling tightly, on the stitch as well as the wraps.
Because coiled basketry is made in a spiral, it is difficult to end it perfectly! It is a good idea to finish the coiling directly above the place where you start gradually bending the sides upward. I also cover the end with buttona, or a piece of costume jewelry, or even a shell (as in the basket on the lower right). You can use glue to add the decoration, or clear nylon thread, which is how I attached the shell.
The coaster, lower left, was made with a cotton yarn, and works very well as a platform for an ice cold drink.
Click here to link to my directions to make a coiled basket.