You need a nameserver. That's what connects a domain name with a server.
You can do that all yourself by installing
bind9 on your server and setting it up but this is usually a pretty poor idea. They need to be online 100% (more than the server itself) and they need to respond really quickly. You'll also need two distinct IP addresses. These are qualities that are just easier to accomplish through managed DNS services.
Many registrars provide nameservers these days (mine certainly do) and even more hosts (I'm not sure who owns your server so this might not apply) provide it for free too. Failing that, there are other third party options like EasyDNS and ZoneEdit, ClouDNS, etc. These are massively available services. They're doing it better than you ever could.
Anyway, once you have that in place, point the domain to the nameserver and then you can set up domain records on the nameserver. This allows a browser to resolve an IP address for a given domain name.