You will need a hosting and a domain. I suggest you to take a tour at this link. http://codex.wordpress.org/New_To_WordPress_-_Where_to_Start
You can build your site locally on your own computer, if that’s what you mean. See the Localhost Installs forum for more info.
Once it’s built you’ll have to move it to a hosting server and purchase a domain in order for anyone to see it.
No, you don’t need a Domain of your own to install and run WordPress for the world to see. Every hosting company that I’ve used has an “alternate” URL that you can use to access the web space they give you. You could use that alternate URL as your WordPress URL.
Unfortunately, most hosting companies make it difficult to set up an account with them WITHOUT your own domain name. You can “tell them” that you have a (fake) domain name registered elsewhere, and they’ll set you up to use it on their site. Once you’ve had your WordPress up and running, you could decide on a domain name, but most hosting companies make it very difficult to change the fake one you gave them initially, though I have had more success adding the domain name I later decide I want as a free “Add-On Domain”. But that (restrictions imposed by web hosting companies) is another discussion.
The fact still remains that you don’t need “your own” (i.e. – unique) domain name to run WordPress.
thank you for you answers, I recently installed WordPress on my Localhost server. I’m just going to develop my pages, and then FTP it to some other Domain.
Thanks to everybody
Tawfiq.