The most popular way to interface with Office 365 email is via the Outlook Web Access portal at https://outlook.office365.com/owa/yale.edu. Just log in using your Yale email address and your NetID password.
Our recommendation to individuals using either MacOS or Windows operating system, and looking for a local software installation option, is to use Outlook for Office 365; you can find information on obtaining the installer here. Additionally, you can obtain a personal subscription to Office 365 at a steeply discounted price with the Microsoft Home Use program.
iPhone/iPad and Android users can download the Outlook app for free from the App Store or Google Play Store respectively.
See also:
Office 365 email: Adding your account to Outlook on the Windows Operating System
Office 365 email: Adding your account to Outlook on the Mac Operating System