This is a great step by step tutorial that teaches you how to crochet in the round. Follow these simple steps and you'll be able to crochet a lovely pattern.
Steps:
1. Chain a ring on which to build your crochet in the round: chain 5, slip stitch to join.

2. Chain 2 to begin to double crochet.

3. Make the required number of double crochet stitches for the round. In this case 10 double crochet, plus the chain 2.

4, 5, and 6. Slip stitch to join. Slip stitch into the top of the chain 2 at the beginning of the row. (See below, step 15 and 16 for the correct stitch to slip stitch into).

7. Chain 2 to begin the next round of stitches.

8. Turn the work to go in the other direction. (You may also crochet in the round in spiral fashion, in which case you do not turn.)

9. and 10. Complete the required number of stitches for the round. (In almost all cases, you will be increasing stitches in this round.)

11, 12, and 13. Slip stitch to join the round.

14. Close-up of the stitch to slip stitch into in order to have an invisible seam.

15. The arrow points to the correct stitch in which to make the slip stitch to join. The most common error in crochet in the round is slip stitching in the wrong stitch. The arrow in photo 15 points to the correct stitch in which to make the slip stitch to join.

16. NOTE: In photo 16, see that the hook actually passes under two strands of yarn. It may seem that you have gone over one stitch too far, however, the stitch before this one does not have two strands to pass the hook under.

17. Photo 17 shows a 3 row round, with no obvious area of the slip stitch and turn.

Read about Harrington's bio and her experience with crochet.