First you should make sure the floor you are removing does not have any asbestos in it . That should be taken care of by a professional. Then the first layer of wood under your vinyl is called underlayment . The subfloor is the term used for the main wood attached to your joist. Do not take up the main layer. Professional normally leave vinyl and underlayment renail it and go over it with new 1/4 " B C grade underlayment, then the new floor.