1. Login to the on-premises Exchange Admin Center.
2. On the Recipients > Mailboxes panel, click the drop-down to add an Office 365 Mailbox.
3. Fill out the webpage to create the new user object in AD and click Save. This will also create a mail-enabled user in Exchange on-prem with a remote delivery address (targetAddress) configured for the tenant address (user@domain.mail.onmicrosoft.com). This will configure the mailbox for coexistence with Office 365.
4. Allow synchronization to occur between Active Directory and Azure Active Directory. By default this happens every 30 minutes by default with AAD Connect. Read http://http://www.expta.com/2016/03/how-to-schedule-and-force-sync-updates.htmlthis article to learn how to force AAD Connect to perform a manual sync.
5. Sign in to the Office 365 portal and assign a license to the user for Exchange Online. At this point the mailbox is created and the user is allowed to sign in to Office 365.

The above method is ideal, but let's say you already have an AD account created. You will not be able to create an o365 mailbox that works using the above method. In that case

- Log in to o365 admin portal and assign a license to the user (assuming it has synced) - Log in to your on-prem Exchange server via powershell and run the command: Enable-RemoteMailbox "User Name" -RemoteRoutingAddress "username@premdomain.mail.onmicrosoft.com"