Author: mahmood

In your sign-in activity’s onCreate method

// Configure sign-in to request the user's ID, email address, and basic
// profile. ID and basic profile are included in DEFAULT_SIGN_IN.
GoogleSignInOptions gso = new GoogleSignInOptions.Builder(GoogleSignInOptions.DEFAULT_SIGN_IN)
        .requestEmail()
        .build();

// Build a GoogleSignInClient with the options specified by gso.
mGoogleSignInClient = GoogleSignIn.getClient(this, gso);

Start the sign-in flow

@Override
public void onClick(View v) {
    switch (v.getId()) {
        case R.id.sign_in_button:
            signIn();
            break;
        // ...
    }
}

private void signIn() {
    Intent signInIntent = mGoogleSignInClient.getSignInIntent();
    startActivityForResult(signInIntent, RC_SIGN_IN);
}

@Override
public void onActivityResult(int requestCode, int resultCode, Intent data) {
    super.onActivityResult(requestCode, resultCode, data);

    // Result returned from launching the Intent from GoogleSignInClient.getSignInIntent(...);
    if (requestCode == RC_SIGN_IN) {
        // The Task returned from this call is always completed, no need to attach
        // a listener.
        Task<GoogleSignInAccount> task = GoogleSignIn.getSignedInAccountFromIntent(data);
        handleSignInResult(task);
    }
}

private void handleSignInResult(Task<GoogleSignInAccount> completedTask) {
    try {
        GoogleSignInAccount account = completedTask.getResult(ApiException.class);

        // Signed in successfully, show authenticated UI.
        updateUI(account);
    } catch (ApiException e) {
        // The ApiException status code indicates the detailed failure reason.
        // Please refer to the GoogleSignInStatusCodes class reference for more information.
        Log.w(TAG, "signInResult:failed code=" + e.getStatusCode());
        updateUI(null);
    }
}

References
https://developers.google.com/identity/sign-in/android/sign-in