This is a *huge* topic! I suggest you get a book on installation, configuration and use of a domain server. If you are interested in a Windows based server product I suggest you go to your local bookstore, go to the computer section, and you will locate books on Server 2003 and Server 2008.
No, a server OS is not free, it is rather expensive. There IS SBS or Small Business Server. That may meet your needs better than a full server product. SMS is for smaller needs of course, but still has plenty of power to run a small domain. The enterprise solutions are mainly for large, well, enterprises.
There are all sorts of modules you can purchase to run on your server. Be sure to buy a solution which allows you to run virtual servers too. It is expensive upfront but is more cost effective down the road when you need to expand.
Here is a link to a search results page with lots of information:
http://search.live.com/results.aspx?q=Windows+Server+solutions&sourceid=Mozilla-search&form=CHROME
Do research there, and then you will have a better idea what you face.
Running a server takes a lot of resources. You will need to run a 64 bit OS server version if you are going to need a lot of power. 64 bit is the newest version, and someday we all will be running these OS versions from homes to businesses, go college campuses to governments and hospitals. Many already are, especially gamers.
If you have a supported motherboard you can run up to 128 gigabytes of RAM with a 64 bit OS, so you can see how powerful one can be. Server solutions need a lot of resources. Don't make the mistake of buying an ordinary PC to house a server.
Good luck and have a nice day.
*edit* Active Directory is only a single module of a server application. Active Directory runs all of your users, keeps track of profiles, and roaming profiles and allows the use of Group Policy. There are many different needs for a company, and finding what these needs are and which products will best suit those needs in the first step in deploying a server and creating a domain. A domain is basically simply the business entity itself, the name of the business so to speak which the computers all hook up to and communicate within the company intranet, and externally to the internet.
Just check them all out and you will see what I mean. It would be far too involved to attempt to outline all the many different configurations of a domain environment here. Larger companies need several servers to run. A web server is within the main server, and runs the company website, both on the internet and the intranet. There are many other modules too. A web server application is only one type of server module. If you do not expect to run a website there isn't any need to setup a web server, but most businesses need a website presence on the web these days or they will not be successful.
In a network without a Server, you can connect up to ten computers. It becomes unmanagable after ten and that is when a server is needed. A domain hooks up more than ten computers. Ten is the base number, so I am unsure where anyone would get the idea that a Server OS which nearly a $1,000.00 or more is spent can only have five (5) Client computers. Client computers or other devices are what your Users would use. The company president, vice president, treasurer, and all their secretaries, plus the accounting department, and the office managers and their data entrants, etc, computers and all the peripherals add up quickly. So, no, far more than a measly 5 clients hook up to one Server machine.