Both Escoce's and Elendil's answers are great: the key is a sharp knife, and the vast majority of people (in my experience) do not have very sharp knives in their kitchens. When people come over to my kitchen and try to cut something they are often shocked at how easy it is. If your knives slide off of food (like onion skins or tomato skins) rather than cut cleanly into them, they aren't sharp enough to make slicing easy.
The one thing I would add is to start with a long knife, and learn the "rocking" chop motion first with it. That is, keep the end toward the tip of the knife on the cutting board, and only lift the back end of the knife high enough to clear the carrot. With a smaller knife, you need to do what Escoce mentions and make an "orbital" motion rather than straight down. I think that's harder to do properly for beginners, so start with a big knife and rock it until you get the hang of it.
I tend to use a 10-inch chef's knife to chop carrots; minimum of 8-inch. Lots of people see such big knives and think they are too scary to use. But they really make chopping incredibly easy, especially if they are kept sharp. With a big sharp knife, you should barely feel like you need force at all to slice quickly through a carrot.