First, you (a prospective registrant) visit a registrar to purchase and register a domain name. You search to find an available name, then request registration of that domain name. The registrar will then contact the registry to register the domain. The registry will then inform the registrar on the availability of the domain name. If the name is available, the name will be added to your shopping cart to be registered. If it is not available, then it’s already registered and owned by a third party. In some cases, you can try to purchase the name from the existing registrar. In other cases, you might have to contact the existing registrant directly to negotiate a price for the name.
Like any other industry, registrars vary in price and quality of service. Some registrars operate in high volume with low margins, so they’re relatively cheap. Others are a little more expensive but offer more bells and whistles. When making a decision, you have to think about what you’d like to accomplish with the domain after you register it. Does the registrar offer hosting solutions, email, website builders, etc.? You also need to consider the price of registration versus the price of long term maintenance of your website. Some more expensive registrars offer ongoing services after registration that may balance out the price over time.