// MainActivity.java
package ...
import android.content.Intent;
import android.os.Bundle;
import android.support.design.widget.FloatingActionButton;
import android.support.design.widget.Snackbar;
import android.support.v7.app.AppCompatActivity;
import android.support.v7.widget.Toolbar;
import android.util.Log;
import android.view.View;
import android.view.Menu;
import android.view.MenuItem;

import com.google.android.gms.auth.api.Auth;
import com.google.android.gms.auth.api.signin.GoogleSignInAccount;
import com.google.android.gms.auth.api.signin.GoogleSignInOptions;
import com.google.android.gms.auth.api.signin.GoogleSignInResult;
import com.google.android.gms.common.ConnectionResult;
import com.google.android.gms.common.SignInButton;
import com.google.android.gms.common.api.GoogleApiClient;

public class MainActivity extends AppCompatActivity implements
        GoogleApiClient.OnConnectionFailedListener, View.OnClickListener {
  
  private static final String TAG = "MainActivity";
  private static final int RC_SIGN_IN = 9001;
  private GoogleApiClient mGoogleApiClient;

  @Override
  protected void onCreate(Bundle savedInstanceState) {
      super.onCreate(savedInstanceState);

      <省略>

      // Button listenersの設定
      findViewById(R.id.button_sign_in).setOnClickListener(this);

      // Google Sign-Inの設定
      GoogleSignInOptions gso = new GoogleSignInOptions.Builder(GoogleSignInOptions.DEFAULT_SIGN_IN).requestEmail().build();
      mGoogleApiClient = new GoogleApiClient.Builder(this)
              .enableAutoManage(this /* FragmentActivity */, this /* OnConnectionFailedListener */)
              .addApi(Auth.GOOGLE_SIGN_IN_API, gso)
              .build();

      // Google Sign-Inボタンの設定
      SignInButton signInButton = (SignInButton) findViewById(R.id.button_sign_in);
      signInButton.setSize(SignInButton.SIZE_STANDARD);
      signInButton.setScopes(gso.getScopeArray());
  }

  <省略>

  // Sign-Inした結果を受け取る処理
  @Override
  public void onActivityResult(int requestCode, int resultCode, Intent data) {
      super.onActivityResult(requestCode, resultCode, data);

      // Result returned from launching the Intent from GoogleSignInApi.getSignInIntent(...);
      if (requestCode == RC_SIGN_IN) {
          GoogleSignInResult result = Auth.GoogleSignInApi.getSignInResultFromIntent(data);
          handleSignInResult(result);
      }
  }

  // Sign-Inした結果を扱う処理
  private void handleSignInResult(GoogleSignInResult result) {
      Log.d(TAG, "handleSignInResult:" + result.isSuccess());
      if (result.isSuccess()) {
          // Signed in successfully, show authenticated UI.
          GoogleSignInAccount acct = result.getSignInAccount();
      } else {
          // Signed out, show unauthenticated UI.
      }
  }

  // Sign-In処理
  private void signIn() {
      Intent signInIntent = Auth.GoogleSignInApi.getSignInIntent(mGoogleApiClient);
      startActivityForResult(signInIntent, RC_SIGN_IN);
  }

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

// content_main.xml
<com.google.android.gms.common.SignInButton
  android:id="@+id/button_sign_in"
  android:layout_width="wrap_content"
  android:layout_height="wrap_content"
  android:layout_below="@+id/textView"
  android:layout_alignParentStart="true"
  android:layout_marginTop="100dp" />