I would like to set up a server similar to Google's. Their domain acts like a double domain, like you can use these URLS, "play.Google.com" or "apps.Google.com", to go to different sites.. For example, my domain would now be "my_domain.com" but i would like another one to be "domain2.my_domain.com". My question is,what is this officially called and how do i set it up? I'm not sure if you need two servers or just 1;
To set up a sub-domain, you need access to the Domain Name Service that is the master for the domain.
You do not need two servers though sub-domains can be on different servers, they don't have to be.
When you purchase a domain name, you will normally get a web interface supplied by the registrar that will let you set up whatever sub-domains you like.
If your domain name is supplied by your ISP or a hosting service, they may not give you access to the DNS settings though you may be able to request that a sub-domain be added - it depends what service you've signed up for.
I would always recommend that you register domains through a specialist domain name registrar. That way, if you fall out with your ISP or hosting provider, you still have control over the domain name.
If you do have access to the DNS. You need to create an "A" record against the domain. It is pretty straight-forwards. As @John Conde said, if you can say what tools you are using, we could help further.
There are quite a few related answers that you'll see in the "Related" sidebar ->
They're called subdomains and you don't need multiple servers to do this. Your control panel software should make this trivial to do. Tell us what software you're using (cpanel, plesk, etc) and I'll update my answer accordingly.
Instructions for setting up a subdomain in cPanel
It is easy, well sort-of, they are called subdomains and most cheap providers will let you create anywhere from 0 to unlimited of them on your web-service. Pretty much how they work is you get a server and get it a static ip. Then, you create an A record that points to that static ip. The web-server such as Apache2 then will take a look at all things coming in on that domain and will route it appropriately to the directory on the system. It is also possible to have multiple servers is just to create A records with a fully-qualified domain so something like
It is also intreresting to note that in the begginng the reason for the www in front of the domain was used to specify that it was the server named www on that domain that would answer the request. The same hold true today except it can now be omited or it can be answered by the same server.