The carrot is very simple and easy. The only hard part is the size. It can be a little tricky if you aren't used to working in very small rounds or with smaller hook sizes.
I used embroidery thread and a 2mm crochet hook to create a finished carrot of around one inch long. But you really can use any yarn and hook you want, so use what's most comfortable for you, or play around with different yarn weights and hook sizes until you come up with a carrot size you're happy with.
Embroidery thread (or yarn of your choice) in orange and green.
2mm crochet hook (or hook of your choice.)
With orange, chain 2
Round 1: Work 4sc in 2nd chain from hook. (4)
Round 2: [Increase in first sc, sc next] twice. (6)
Round 3-5: Work one sc in each stitch around. (6)
Stuff your carrot lightly.
For the leaves--
Join green to any stitch using a slip stitch.
Chain 7, sl st in 4th ch from hook, sl st in each of next 2 chains. sl st to top of carrot. Slip stitch to another sc and chain 7 again to create the next leaf. Carry on in this way until you have 3-4 leaves.
Finish off leaving a tail for sewing. Sew around the top of the carrot to close up the hole and cinch the leaves together.
Voila! You're done. :)
To make your carrots longer, just add more rows. If you want them a little fatter, try increasing to 9 stitches after a row or two of 6.