From elsewhere:
Carrot seed is fairly easy, provided you don't have any wild carrot ('Queen Anne's Lace') growing nearby.
Carrots flower in their second year, so you need to dig up your carrots in Autumn.
Lay them all out so you can compare them, and select the best 40 roots:
Make sure you choose ones that are true-to-type: right colour, shape & size. You can even test the taste by slicing off the tip!
If your area has cold winters, store them in sand or sawdust in a cool but frost-free place, and plant out in spring.
(the ideal is about 5-10 C and 95% humidity)
In particularly mild areas you can replant them straight away where you want them to grow.
You can plant them quite close together, so 40 needn't take up much space.
(The numbers are really important if you want to get good seed.)
The next summer they will flower (to about 5 foot high!)
MAKE SURE THERE IS NO QUEEN ANNES LACE NEARBY, THEY WILL CROSS!
... and seed is ready in autumn. Just rub the seed off when it is mostly brown.
You will get huge amounts of seed: if you dry it properly (see our seed-saving pages) it will be good for 2 or 3 years.