To remove the key cylinder you have to turn the key to the accessory position, stick a paperclip into the little pinhole on the face of the key cylinder and then turn the key around a little further in the counter-clockwise direction and it will come out. However, I don't think that you have a problem with the cylinder. You say that you just got the car. Did it, by any chance, come with two ignition keys? If yes, then one is for the door locks and the other is for the ignition. People frequently replace the ignition cylinder without replacing the door locks, or vice-versa, and that sounds like what has happened to your car. Hope that helps.