Choosing a domain name (like mycompany.com) is one of the first steps in building a website. The domain name is the "address" for your online site, and is usually purchased from a domain registrar like Namecheap.com at a cost of about $8-10 per year.
To determine if a domain name is already taken, try typing it in at Network Solutions' WHOIS site or the handy SWAMR site highlighted in the next section. Generally speaking, you want to have a domain name that reflects the name of your business or site. For example, my site is binaryarts3d.com because the name of my business is Binary Arts. I would have chosen binaryarts.com but that was taken. It is possible to have more than one domain name that point to the same site, though, so many businesses select something that contains likely search terms related to what they do.
For example, suppose I had a company called Giambruno Plumbing, located in Sacramento. The first thing I would check is if giambrunoplumbing.com was available, and grab it as my domain name. However, since I know that people in the area who might be searching for a plumber are likely to search for the words "Sacramento Plumbing Plumber" or something similar, I can use that to create another domain name in the hopes of coming up near the top of the results for someone doing that search. Here's where a domain name search tool called SWAMR can help.