[thelist] How Host Sub-Domain When Primary Domain Hosted Elsewhere?

[Bob Haroche]

My website example.com is hosted with a 3rd party, and the DNS is
handled by ATT.

I want to host on my own box subdomain.example.com.  ATT will
configure their DNS server to point to my server's IP.

What do I need to do on my end in terms of DNS?

I believe if I wanted to host only the single subdomain.example.com
and nothing else, I wouldn't need a DNS server, but simply place my
subdomain website in my Apache web root. However I do want to host
multiple subdomains and maybe a couple of primary domains as well.
Hence I need to set up DNS on my box, right?

The web hosting isn't an issue -- I already have the apache virtual
hosts configuration ready. And I can handle primary domain DNS
hosting, but I've never handled subdomain DNS hosting when I wasn't
also handling the primary domain DNS hosting. So what type of DNS
records (for web serving; no mail or ftp) do I need on my end in this
instance (and again the DNS host for the primary domain is
cooperating):

SOA for the subdomain?
NS for the subdomain?
A for the subdomain?
CNAME for the subdomain?

Thanks in advance,

Bob