If you are the delegate on an email account you will see it listed under your own Gmail avatar.
Click on your avatar at the top right corner of your email window. A list will drop down of any account that you are a delegate on. Click on the one you want and it will open in another tab so you'll be able to keep your own email AND the second email open at the same time.
Troubleshooting: If you've been told you're a delegate but you're not seeing the account, refresh your email window or restart your browser.