The detailed process of registering a domain is described here, however, applying for a domain name requires 3 simple steps:
1. Check if your chosen name is available:
2. Choose a registrar!
Registrants are served by registrars, who provide the necessary customer contact and background services. The Registry is not in direct contact or contract with the registrants.
You can find the list of registrars here.
3. Register the name at the chosen registrar
Contract with the registrar of your choice based on its contractual terms.
You can find out the detailed registration process here.