Each computer on the Internet is identified by an “IP address” (IP = Internet Protocol), which represents a string of numbers separated by dots ranging from 0 to 255.
» Example: 205.207.161.214
Unfortunately, those numbers are hard for us to remember, so an IP address can be assigned one or more domain names, i.e., you can have more than one name point to one IP address.
To see if a name is available a Domain Search is performed and can be done at pretty much any web host’s web site.
In the early days you had to register your domain through networksolutions.com (it was the ONLY option), now there are many different sites to choose from with varying services and rates.
Registering a name means you have the right to use it and you are basically renting it every year. Yes you have to pay for it every year, if you stop paying or do not renew you can lose the name.
Now days you can buy names from various sources from web hosts bundling names with their hosting packages to resellers. As with anything it is buyer beware – read the fine print.
To look up information on owners of web address you can go to whois.com.