Visit the website of any Registrar and register your domain name by using a credit card for payment. Register a domain through some domain registration service provider and furnish him with all the details related to the domain name. The registration provider will register the domain on your behalf with the details that you provide.
Most registrars have an automated registration process that you initiate from their Web site. Once you apply for the domain name, the registrar accepts payment, processes the order, and then the domain name is registered to you. This process can generally be completed within one business day, but it will vary by registrar.