I am going to be rather general since there is a lot I do not know about your specific scenario.
If it just for your access, you can use the host file on your client computer. I do not do this but a friend of mine uses host files exclusively and has for more than 20 years. You can check out: http://en.wikipedia.org/wiki/Hosts_(file)
I use a separate internal DNS server for my work. You can install Bind or other DNS software on your web server if you are not making it public. If you are making it public, then I would use a DNS host. This is because I would not open DNS vulnerabilities on my web server if it was public.
If you already have a domain name hosted, and you want to use a sub-domain, then you can use a CNAME or A record to point to this server. If you do not have a domain name hosted, then consider registering a usable domain name (if you want to) and creating a record in a DNS host.
Each DNS host has a different interface so I cannot get too specific on this. I have not kept up with these too much.
If the server is not to be public, make sure you are using a non-routable IP address such as 10.0.0.100 to help keep it private.