Problem with permissions / protocols

If I share directories on an NT box with people on the LAN, how do I grant them access if they are not explicitly added as a user to the NT box? One of the problems I am having is that the users cannot even get to the point where they can select a directory to map a drive to, attempt to map it, and be asked for a user id and password. Could this have something to do with my attempt to do this over TCP/IP only?