You can harvest carrots as soon as you notice little carrots worth bothering with in your thinnings. As you keep weeding and thinning, you'll notice the carrots getting bigger. Enjoy them at any size.
Most seed labels list "days to maturity." That means the crop should be fully developed around then. If you're planning to store some of your harvest, wait until then to pull them.
I don't know where you live and garden, Laura, but there's still plenty of time to mature another crop of carrots in most parts of the U.S. if you sow them now. Remember, you have many varieties to choose from. Some carrots grow very quickly; these tend to be snappier and tenderer than the long or fat ones intended for long storage. Part of the fun of gardening is trying different varieties and discovering which ones best suit your tastes and needs.