Pick a needle several sizes larger than recommended for the weight yarn you are using. I used a worsted weight wool and a size 11 needle.
Start by knitting a rectangle in garter stitch. Size does not matter. Remember you are playing with scraps!
When you finish the rectangle do not bind off. Instead pick up stitches on the other 3 sides of the rectangle using a circular needle (I used a 24-inch size 11). Join in the round and just knit!
Continue knitting. It will naturally look like stockinette stitch because you are knitting in the round only using the knit stitch! This is the beauty of knitting-in-the-round!
As your basket grows decrease a few stitches evenly around (I used several knit-2-together). Continue knitting.
When you feel that it is tall enough bind off all stitches loosely and weave in the ends.
The fun begins when you toss your project in the washing machine with a pair of old jeans, some detergent, and hot water. Wash everything! You may want to put the basket through the wash several times to create a completely felted basket. I usually do 3 runs. Remove your basket and stuff it with plastic bags to help it hold its shape while drying.
Enjoy the process and your basket!