1.) Before you start downloading and installing make sure you have an office 365 license (You can do this by checking with IT) & remove the old office applications by locating them in "Applications" -> right click -> "Move to Trash"
2.) Go to Portal.Office.com and sign in with the users e-mail and domain password.
3.) It will pop up with some tutorial information, you can simply click through or exit out of it. You will than click on "Install Office" -> "Office 365 apps"
4.) Click on the Installer file and follow the install instructions.
5.) Open any one of the 365 apps, in this example ill be using Outlook, click on -> Get Started -> Sign In
6.) Sign in using your full e-mail and domain password than click on "start Using Outlook" -> Add "--Users E-mail--" -> "Done"