How to connect mailbox with Gmail?

Here are instruction explaining how to add email address (one or more) to Gmail.
https://support.google.com/mail/answer/22370?hl=en

Here is a video showing the whole setup process.

If you decided to use POP3 connection as a incoming mail server please note that there might be a delay in receiving emails to your Gmail because your original mailbox will be checked for new mail on intervals every 15 minutes or so, depending on your configuration. Therefore we recommend to setup email redirection in your original mailbox to send automatically messages to your Gmail email address as soon as they arrive.

During set up process you will be asked to provide the following details Incoming and Outgoing mail servers (Host name, Port number, Username and Password). These details can be obtain from you hosting company.

If you are hosting your mailbox with us please use these settings below.

Incoming mail server (POP3/IMAP)

Host name: Your domain name e.g. example.com
Port number: The POP3 port is 110. The IMAP port is 143
Username: Your email address e.g. [email protected]
Password: The one you use to login to your mailbox

Outgoing mail server (SMTP)

Host name: Your domain name e.g. example.com
Port number: The SMTP port is 25
Username: Your email address e.g. [email protected]
Password: The one you use to login to your mailbox