The process of purchasing a domain name is very easy, you just need to visit one from the best domain registrars to buy your domain online. The main problem before purchasing a domain name is the choosing of that domain. We can call this process is the SEO of the domain name.
Before choosing the domain, you should determine the niche of your website firs. I strongly recommend to add the main keyword of your niche in the structure of the domain name. Say that your niche of your website is "Golf Tips" and the main targeted keyphrase is "Top Golf Tips", you should purchase one of the following domains.
TopGolfTips.com, Top-Golf-Tips.com, Top-GolfTips.com and other extensions. Don't purchase a general name because the purchase of such names will not help your new website with search engines.
You can purchase your new domain names from these sites:
GoDaddy.com, NameCheap.com, HostGate.org.