How to log in to personal email account-Google,Yahoo,Hotmail

Question

I am creating an MVC website for a client. I want the users of this website to log in to their personal email account (Google, Yahoo, Hotmail etc) from the website 

and select email ids in their login to send an invitation to the MVC website I am creating.

What is the best way to login to personal email accounts from a website to invite friends in the personal email id?

Thanks,