как вариант вы можете взять вот этот пример из документации
mAuth.createUserWithEmailAndPassword(email, password)
.addOnCompleteListener(this, new OnCompleteListener<AuthResult>() {
@Override
public void onComplete(@NonNull Task<AuthResult> task) {
if (task.isSuccessful()) {
// Sign in success, update UI with the signed-in user's information
Log.d(TAG, "createUserWithEmail:success");
FirebaseUser user = mAuth.getCurrentUser();
updateUI(user);
} else {
// If sign in fails, display a message to the user.
Log.w(TAG, "createUserWithEmail:failure", task.getException());
Toast.makeText(EmailPasswordActivity.this, "Authentication failed.",
Toast.LENGTH_SHORT).show();
updateUI(null);
}
// ...
}
});
https://firebase.google.com/docs/auth/android/pass...