Domain names can only be purchased from an ICANN accredited registrar, such as Dominion Domains, or from an authorized reseller that has a relationship with a registrar.
On the registrar or reseller site, you can search for a specific domain name that you are interested in. Most registrars will also provide suggestions for similar domain names. These will generally provide domain names with different top level domains (TLDs) or extensions (the part to the right of the dot) as well as different second level domains (the part of the name to the left of the dot). These suggestions are especially helpful when the domain name you desire is not available.
Once you find a domain name you want, you simply add it to your cart and check out. After the domain name purchase has competed, you can go into your account to manage DNS settings, name servers, etc.