I don't grow carrots every year. I should, I just don't. They are very easy to grow and the good thing about carrots is that like onions and potatoes they store very good. Today is 10 March 2017 and I am still harvesting and eating carrots from my 2016 garden.
I planted a very small patch of carrots, an area about 30"x36" at most. I planted probably about a hundred seeds in that small area. The idea was to let them grow in densely and pull every other one once they got pinky finger sized. Then the rest would grow into the now open space until they also were crowded and I'd pick every other one again.
I have many critters visiting my yard at night so I have to protect the more tasty plants from rabbits, groundhogs, deer, and sometimes squirrels. This cage works perfect and I got it from a dumpster behind a department store.
Whenever I do decide to plant carrots, I set off a more or less square area with boards or concrete pavers. Then I dig out all the soil down about eight inches. I run all this dirt through a 1/4x1/4 inch screen to remove all the rocks and stones. To this natural dirt I add compost and course sand. This creates a light, airy, loose soil, which is perfect for carrots. The course sand also cuts down on the slug population; they don't like oozing across sharp sand particles.
I scratch out 1/2 inch deep lines (mini-furrows) and drop seeds in every inch. Carrot seeds are really tiny and often times more than one seed drops. That's no big problem, that is a min-carrot that I will harvest early. Then I cover the seeds with white sand. The lines of white sand help me to see what is a carrot coming up and what is a weed. I pick weeds when they are very small so that pulling them does not disturb the roots of my crop plants.
I almost only grow the "nantes" type of carrot. These are short, stocky carrots that can push through heavier soils. I do this even though I have prepared nearly ideal soil for my carrot beds. These carrots are thicker and easier to pull late in the fall and into winter when the more slender, tapered carrorts will often break off as you pull. I also like the flavor of these carrots.
You will often read about how hard it is to get carrot seeds to germinate and they will offer tricks to help this process. I don't do any of that and I get nearly 100% germination within ten days of planting.