Patina
Over time your blade will develop a protective patina. This will add character to the blade showing a unique reflection of its usage. This natural characteristic of carbon steel can be caused by a reaction with acidic food and is a protective layer which will help to stop the blade from rusting.
Washing
Hand wash only - Carbon steel will rust if put through a dishwasher or left to soak in water. Always make sure your blade is completely dry before storing.
Keeping an edge
Chopping on a hard surface will wear and potentially chip the edge. To prevent the edge becoming dull prematurely, always use a wooden or synthetic chopping board.
To keep an edge on the knife I would advise stropping the blade regularly. When this no longer improves the performance it will be time to sharpen the knife on a stone.