As we know that a website is known with it's name. i.e the the website name. So to have a website we need to buy a name for that to denote it. Technically it is called Domain Name. We need to buy it for some finite period of time from any of the Domain name providers. The cost of it will depend on how many years you are buying the domain for.
The it comes to the website. You need to build your website, which the visitors will see on your site. It can be couple of html files or a complex web application.
Now after you build your application, you need to host the application somewhere in a system. For that you need to buy a hosting. You can buy it from several hosting providers in the market.
After you properly run our application in your hosting machine, you need to tell your domain name to point the hosted machine's application whenever that domain name is fired.
For that you need to configure the DNS of the domain you bought. Most of the domain name providers will give you a DNS management tool for this. There you can setup the A Record and Name server records of the hosting machine. After you setup this, it will take 4-8 hours to reflect throughout the world.
And here you go.... Your first site is live.
If you are really planning to own a site, I will suggest you to book your domain name if possible. As domain names are always first come first serve basis. If a domain name is taken, you can't own it.
Good Luck !!!!!