How do I access a gmail account that has been delegated to me?

To access a delegated email account

Once an email account has been delegated to you (or once you have been granted access), you can begin accessing that account from your own account. To do so, complete the following steps:

Log in to your Google Mail account from a web browser (note this isn't available from a mobile device). If you are already logged in to Google Mail, you may need to close out of your session and log in again to update your security token.
Click your account photo or the circle with your first initial in it (located in the upper-right corner of the page).
From the drop-down menu, select the desired delegated account. A new window or tab will open displaying the delegated account. If you don't immediately see the account, you may need to log out of g-mail and log back in again.

NB - You may also wish to set an Out-of-Office reply. This can be done via the delegated inbox.

In the top right, click Settings See all settings.
Scroll down to the "Vacation responder" section.
Select Vacation responder on.
Fill in the date range, subject, and message.
Under your message, check the box if you only want your contacts to see your vacation reply.
At the bottom of the page, click Save Changes.