I'm not 100% sure if you mean how to validate if a string is a valid e-mail address or how to authenticate a user using an e-mail address.
If you want to validate if an entered e-mail address is valid, I'd recommend that you use the Patterns utility class:
String email = "john.doe@gmail.com";
if(Patterns.EMAIL_ADDRESS.matcher(email).matches()) {
// e-mail is valid
}
else {
// e-mail is invalid
}
If you want to authenticate a user using an e-mail address, I'd really recommend that you take a look at how to authenticate a user using oAuth2 and one of the Google accounts on the device. Google engineer Tim Bray has written a very easy to follow guide on the Google Developer blog about how to verify back end calls from Android.
UPDATE: Since you're asking for a way to authenticate a Google or Yahoo account I'll update my answer here:
First of all, I would never ever let a third-party app know the password to my email account. Besides, it would be absolutely crazy to ask for gmail username and password when you are more or less guaranteed to have at least one on an Android device. Check my previous link to learn how to login using a Google account without having to ask the user for his password. It seems as though Yahoo has oAuth support. And there already seems to be a few questions regarding how to integrate this on Android.
