A simple way to crochet a round rug is to use a very chunky yarn, large hook and coiling pattern. Select a durable and thick yarn, like Craft-tee Yarn available at Jo-Ann Fabrics, and pair with a size Q hook.
Start with a slip knot and chain 2. In the second chain from the knot, make 6 single crochet. Join the first and last single crochet in the round with a slip stitch. This is the first round.
For round 2, make 2 single crochet in each single crochet in the prior round, for a total of 12 stitches. Slip the first and last stitches in round 2 together with a slip stitch.
The third round is worked by making 1 single crochet in the first stitch, then 2 single crochet in the next stitch, repeating this pattern all the way around and ending with a slip stitch to join the first and last stitches.
For round 4, work 1 single crochet in the next 2 stitches, then 2 single crochet in the next stitch. Repeat this all the way around for a total of 24 stitches.
Each row increases the distance between the stitches with 2 single crochet in 1 stitch by 1 stitch. The fifth row is worked by making 1 single crochet in each of the next 3 stitches, then 2 single crochet in the following stitch all the way around. Continue this pattern until the rug reaches the desired size, and end by slip stitching the first and last single crochets of the last row together.