First you'll need to log into the Office 365 Outlook Web Client if you haven't already done so. See this tutorial for instructions on how to do that.

Once you log into the Office 365 Outlook Web Client, return back to this tutorial and proceed to the next step.

Click here for a tutorial on how to log into the Office 365 Outlook Web Client

To open the email account that you have been delegated access to, click on your Office 365 user icon in the top right corner.

In the menu that appears, click on Open another mailbox...

In the window that appears, type in the email address of the email account that you want to open up. A drop down menu will appear and the email address should appear as a clickable item. Click on the email address to select it.

In the next window that appears, click on the Open button.

You should now be able to view the inbox for the delegated email account. You should also be able to send new emails from this email account.

If you are unable to send new emails from the shared email account, contact help@education.utexas.edu for assistance. Your email account may need to be granted additional privileges to be able to send emails on behalf of this other email account.