Alternatives to changing your domain
When you sign up for a Google Apps account, you provide an Internet domain name that becomes the primary domain associated with your Google Apps account. You and your users get account names and email addresses at this domain and you can host your website, built in Google Sites if you like, at this domain.
If you just want your current users to be able to receive mail using an address at the new domain, add it as a domain alias and leave your primary domain as is. For details, see Give users an address at another domain.
If you also want your users to be able to send mail using their new address at the new domain, see Send mail from a different address or alias.
Users still have to sign in to their services using their account name at the old domain, but if you set this up properly, they can send and receive mail using an address at the new domain (as well as from the old domain).
To change your users' account names to the new domain, add the domain as a separate domain. Then move users from their current domain to the new domain. After that, users can sign in to their services using an account name at the new domain. They get an email address at the new domain (and no longer have their old email address). They can otherwise use the new account name just like they did their old one.
To get started, see Add users from another domain.
The easiest way to create web addresses at the new domain, such as mail.newdomain.com, or to host your business website built in Google Sites at the new domain, (such as www.newdomain.com) is to add a secondary domain then Customize a Google Apps service address.
Reseller accounts, domains purchased through a Google partner, or accounts with Chrome or Mobile Device Management licenses cannot use the Admin console to change primary domains.
You cannot change Standard edition domains.
Using a mygbiz.com trial domain? If you signed up for a trial domain and want to convert it to a custom domain you own, you can do that without having to create a new account. For details, see Convert a trial domain to a custom domain.