The domain buying process is basically the same for all reliable registrars. You will need to find a domain name, sign up, activate an account, fill in the domain information, and complete the purchase.
Here are guides for purchasing domain names from some popular domain name registrars.
GoDaddy
Type in the domain name you would like to buy and click on Search Domain.
Find the available domain name and click on Add to Cart.
Fill in the credentials and click on Submit button.
Fill in the billing information and click on Complete Purchase.
Done. Your domain name is ready to set up: http://help.tilda.ws/customdomain
