Before you can have a website, you need a domain name. This will be the name of your site. When I designed my site, I bought 2 domain names: the name of my studio (Seven Scrolls) and my own name (Patty Olds). I recommend this approach if you have a studio or business name, because people may see your work at a friend's house and ask who the artist is. The friend will say your name but not necessarily remember to mention your studio...or vice-versa. Many complete strangers have ordered from my website because they Googled my name (which is signed on all my pieces) to find out where to buy my work.
Now you have to make a decision: you can buy your domain name and hosting services from different companies or from the same company. There are many kinds of services, probably thousands, maybe millions, but I tend to use a search engine (Google) and look for third-party opinions on matters like this. I am a relentless researcher and some people don't want to spend that much time, so here are a few of the links I have used:
It's worth reading through these sites because you will learn a lot in a little bit of time. You can often get a deal if you sign up for multiple years with one webhost, and you can get a free domain name registration as well. Of course, you may want to sign up for only one year because as you learn more you may want more options down the road and you won't want to be locked into a contract with a company that doesn't offer what you will be looking for.
If all you are going to do is register your name and make a site for your work, you can get a "shared business web hosting" package for less than $5 a month (you'll have to sign up for minimum one year).
After you have done all the wheeling and dealing and actually have paid for the services, PRINT OUT THE CONFIRMATION and anything else they send you later. You will need this info when you go to publish your site. PRINT IT OUT, MAKE A FOLDER AND DO NOT LOSE this info!
NOTE: there is normally around a 24 hour waiting period after you get your site name before it can go live on the internet, something to do with security...anyway, don't despair, have a little patience and wait a few hours, it'll resolve.