If I register a domain (xyz.com), how is it handled if I would like a members portion of the site to be referenced at members.xyz.com?
Most hosts and registrars allow you to manage your DNS for your domain. Here you should be able to set up sub-domains like members.example.com.
"Members" would be a host in your domain, xyz.com. So in DNS you would create an "A" (or host) record for "members".