First thngs first. Please checkout the link in my signature. It will definately provide you with all of the information you need to get your new cornsnake off on the right foot. It will sort you out as far as general care and husbandry is concerned.
After you checkout that link, if there are any specific questions you have, feel free to ask.
But to answer your original question, yes, you're snake eats pinkies. On average a snake will eat a pinky that is about 1.5 times larger than the widest part of the snake's body. And they will typically eat one of these every 4-5 days.
It is best to feed outside of the enclosure in a seperate deli cup, plastic tub, or similar large "dish" to prevent the opening of the lid and your hand from being associated with feeding, as well as to prevent any accidental ingestion of the tanks substrate. Obviously if you're using astroturf, ingesting substrate isn't going to be a problem.
Good luck and enjoy your new pet!!