How do I buy a custom domain through Blogger?

You can buy a domain from the Settings | Publishing tab,. Just select the Custom Domain option, enter the domain name you'd like and click Check Availability. This will take you to the Google Apps domain purchase website, which will let you know if the domain is available and proceed with the registration if it is. Finally, you'll go to Google Checkout where you'll make your payment. Your domain is registered with one of our registration partners, either eNom or GoDaddy.

Now Register your Domain:

Enter the Domain registration form:

 

Now Add a credit card to purchase:

Finally you place the order

You'll get a domain registration confirmation email from Google Apps. Clicking the link in this email allows you to sign this domain up for an Apps account. Google Checkout will also send you an email with the order receipt.