Chromebooks have no installed mail client, so you have two options.
WEBMAIL
Visit yourdomain.com/webmail and log in with the full address and password. Nothing to install, works immediately, and handles folders, filters and contacts.
Add it as a bookmark or a pinned tab. For many Chromebook users this is enough.
THE GMAIL WEB INTERFACE
Add your domain mailbox to an existing Gmail account, receiving by POP3 and sending by SMTP. See the article on using Gmail with your domain email.
This gives you the Gmail interface and offline access, at the cost of a delay on incoming mail.
ANDROID APPS ON CHROMEOS
Where your Chromebook supports Android apps, install Gmail or another mail app and configure it exactly as on a phone, using IMAP.
WHICH TO CHOOSE
Webmail for simplicity and immediate delivery. Gmail integration if you already live in Gmail and can tolerate the collection delay.
Bookmark the webmail address rather than searching for it each time.
