You've decided that you want to have a website of your very own. Great! Now what?
First, you're going to need a web address. That's the address that people type into their web browser to get to your site. That address can either be a subpage on someone else's domain (ie: www.facebook.com/mercyloomis or www.myisp.com/bobsauthorpage), or else you can have your own domain name (ie: www.mercyloomis.com).
The nice thing about a subpage is you can probably get one for free or very cheap through the company you get your internet through. However, it's not quite as professional (or satisfying) as having your own name in that address.
You can't own a domain name, you just rent it. (Yes, this costs money.) All internet domain names are handled by domain name registrars which are overseen by ICANN. Examples of domain name registrars are GoDaddy.com and Network Solutions. Since you're getting the same domain name (the one you picked, if it's available) regardless of which registrar you go through, the main difference between them is in the packages offered, customer service/support, and the pricing. Do your homework. For myself, I got recommendations from my IT buddies as to what service they liked.
Choose a web address that will work for you: either your name/pseudonym, or the name of your book if the website is to promote a particular release. Personally, I think you get the most bang for your buck by starting with your name/pseudonym. You can always add pages later for your books.
If the www.yourname.com that you want is already taken, you can always try www.yournameauthor.com or www.yournamewrites.com, or another similar variation. If too many of those are taken, you may want to consider using a pseudonym that's a little less common.