Carving is all about leaning toeside or heelside, to get your board to turn in that direction. It's really simple. Push your board, and while rolling, put weight on your heels. You will slowly turn that direction. The harder you push on your heels, the sharper your turn will be. While skating around, you will be using this a lot. Go out to the street or parking lot, and try pushing forward and carving around things. Try pushing right at something that you don't want to hit, like a curb, and see if you can carve around or away from it.
If you lean your upper body toward the direction you want to carve, you will find it even easier. Carving on a skateboard is very similar to carving on a snowboard, except that you don't catch your edge and die like on a snowboard! If you want to carve especially deep, try bending your knees a lot, and crouching low on your board. Carving is easier on a longboard, but it is a valuable skill in any board sport.