Assuming I used python, I'd just import a library for sending email, or if using C# just import System.Net.Mail. Then it should be pretty simple. I would have made sure it worked for a major email provider (like gmail) and then work on edge cases when/if they came up.

Since the game would need your email password in order to load incoming messages I would advise them to create a new email just for game communication purposes anyway, and tell them not to use certain characters if for some reason I couldn't get them to work (although the libraries should be able to handle it anyway).