Step 1: Make sure you're logged in to Mail with a Microsoft account. If you're using a local account to log in to Windows 8, you'll need to log in to Mail with a Microsoft account before you can add other e-mail accounts.
Step 2: From within Mail, use the Win+I shortcut to quickly get to Mail settings, then click on Accounts.
Step 3: Click on Add an account, then choose the e-mail provider you want to add.
Step 4: Enter your log-in credentials for the e-mail account you're adding, then click Connect.
That's it. What do you think of the Windows 8 Mail app? Do you see yourself using it or are you going to stick with the Web client?