Making my DNS valid for domain names

[Creighton Fox]

I'm a small web host, and I want to run my own DNS (like 
ns1.mydomain.com) so that all the domains we host can use that as their 
DNS.  I have bind set up on my machine (actually our hosting software 
handles it).  I've found plenty of good bind tutorials, but nothing 
that answers the question I really need answered.  It's a bit long 
winded, but if you could answer my question I'd be very appreciative.

How do I get my DNS recognized as a name server?  If I do a 'dig' on 
everydns, it shows their name servers as ns1-4.everydns.net.  How do 
people know where to find everydns.net?  It seems to me that they would 
never be found, because if they can't find everydns.net, they certainly 
can't find ns1.everydns.net.

So if I'm mydomain.com, and I want to have my ns be ns1.mydomain.com, 
how do I tell the more upper level name servers what the IP of 
ns1.mydomain.com is?

If this doesn't make any sense, please let me know.  I've been 
searching and racking my brain on this for over a month now, and no one 
seems to be able to help me.

Thanks!