Your domain name (for example,"www.mystore.com") must be 32 letters or less, including the extension, which is the part following the dot. The most popular extensions are .com for commercial sites and .org for nonprofit sites. Many of the most appealing .com and .org names have been taken already. Consider these alternatives:
Outside the U.S., you can take a country's extension, for example, .ca for Canada. Here's the full list of domain extensions.
Otherwise, if you choose to change your hosting company, you will be unable to access your record in order to point your URL to the new location. If you are registering the domain yourself, be sure to retain the email address you used to register it. That's your ID.
Many companies, such as myhosting.com offer a free Domain with an annual hosting plan.
You go to the registrar's website. You fill in the name you want and click the button. The registrar will tell you whether the name is available, or suggest others. Once you have a name that's not taken, you purchase it just as you would on any ecommerce site.
Search engines will place heavy weight on your site name in deciding what your site is about. If your site is about coffee cups, try to reserve a name like "coffeecupsbyandy.com." That will increase your site's visibility.
If you are setting up a free page, you probably won't have your own URL. Your web address will be a subset of the URL of the company hosting your page. On Yola, for example, your address will be www.yolasites.com/ThisIsMyWebsite.