You have to purchase the dot-com or dot-co.uk domain names. You can usually get free web hosting from your ISP, and depending on who they are you can control your site's appearance. I currently use my ISP's free facility for a website which I write in dreamweaver and upload using the ISP's ftp passwords, which they supply happily. However as there is no such thing as a free lunch, you can't control all of the free website's domain name, so there will be an element of the ISP's name alongside your own identity. A good example of this kind of arrangement is at
http://www.a.jackson.btinternet.co.uk