Alright, let's get started with enabling the Email/Password sign-in method in Firebase. Head over to the Firebase console, click on the 'Develop' menu, then find the 'Authentication' card, and finally, hit the 'Sign-In Method' tab. In the list of sign-in methods, look for Email/Password, click on it, and set it to 'enabled'. Easy peasy!

Now, to get your Android or iOS app chatting with Firebase, you'll need to add some Firebase libraries to your project. These dependencies are like the bridge between your app and Firebase.

For Android:
Open up your app level build.gradle file and add this line:

implementation 'com.google.firebase:firebase-auth:20.0.3'

For iOS:
Pop open the Podfile and add this:

pod 'Firebase/Auth'

Before diving into Firebase authentication features, you need to create a Firebase authentication instance. This instance is your gateway to all the Firebase Auth goodies.

For Android:

FirebaseAuth auth = FirebaseAuth.getInstance();

For iOS with Swift:

let auth = Auth.auth()

Once you've got Firebase Authentication initialized, you can use the createUserWithEmailAndPassword method to create a new user with an email and password. Just pass in the user's email and password as arguments.

For Android:

auth.createUserWithEmailAndPassword("[email protected]", "password")
    .addOnCompleteListener(this, new OnCompleteListener<AuthResult>() {
        @Override
        public void onComplete(@NonNull Task<AuthResult> task) {
            if (task.isSuccessful()) {
                // Sign up successful
                FirebaseUser user = auth.getCurrentUser();
            } else {
                // Sign up failed
                Toast.makeText(MainActivity.this, "Authentication failed.", Toast.LENGTH_SHORT).show();
            }
        }
    });

For iOS with Swift:

auth.createUser(withEmail: "[email protected]", password: "password") { authResult, error in
  if let error = error {
    print("Failed to sign up: \(error.localizedDescription)")
    return
  }
  // Sign up successful
}

Remember to swap out "user@example.com" and "password" with the actual email and password provided by the user.

After a user signs up, you can check if everything went smoothly. If it did, you can grab the user's information.

For Android:

if (task.isSuccessful()) {
    FirebaseUser user = auth.getCurrentUser();
    // user is signed up and logged in, do something with user object
} else {
    // there was an error with sign-up, handle error
}

For iOS with Swift:

auth.createUser(withEmail: email, password: password) { authResult, error in
if let error = error {
    // Handle sign-up error
    return
}
if let user = authResult?.user {
    // User is signed up, do something with user object
}
}

And there you have it! You're all set to get your users signed up with email and password using Firebase. Happy coding!