RetrieveAccessTokenActivity.java

package com.google.devrel.samples.gmstest.app;

import android.app.Activity;
import android.content.Intent;
import android.os.AsyncTask;
import android.os.Bundle;
import android.util.Log;
import android.view.Menu;
import android.view.MenuItem;
import android.view.View;
import android.widget.TextView;

import com.google.android.gms.auth.GoogleAuthException;
import com.google.android.gms.auth.GoogleAuthUtil;
import com.google.android.gms.auth.UserRecoverableAuthException;
import com.google.android.gms.plus.Account;
import com.google.android.gms.plus.Plus;

import java.io.IOException;


public class RetrieveAccessTokenActivity extends Activity implements View.OnClickListener {

    private static final String TAG = "RetrieveAccessToken";
    private static final int REQ_SIGN_IN_REQUIRED = 55664;

    private String mAccountName;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_retrieve_access_token);
        findViewById(R.id.button_token).setOnClickListener(this);

        // Manual integration? Pop an account chooser to get this:
        mAccountName = "me@example.com";
        // Or if you have a GoogleApiClient connected:
        // mAccountName = Plus.AccountApi.getAccountName(mGoogleApiClient);
    }

    @Override
    public void onClick(View view) {
        if (view.getId() == R.id.button_token) {
            new RetrieveTokenTask().execute(mAccountName);
        }
    }

    @Override
    protected void onActivityResult(int requestCode, int resultCode, Intent data) {
        if (requestCode == REQ_SIGN_IN_REQUIRED && resultCode == RESULT_OK) {
            // We had to sign in - now we can finish off the token request.
            new RetrieveTokenTask().execute(mAccountName);
        }
    }

    private class RetrieveTokenTask extends AsyncTask<String, Void, String> {

        @Override
        protected String doInBackground(String... params) {
            String accountName = params[0];
            String scopes = "oauth2:profile email";
            String token = null;
            try {
                token = GoogleAuthUtil.getToken(getApplicationContext(), accountName, scopes);
            } catch (IOException e) {
                Log.e(TAG, e.getMessage());
            } catch (UserRecoverableAuthException e) {
                startActivityForResult(e.getIntent(), REQ_SIGN_IN_REQUIRED);
            } catch (GoogleAuthException e) {
                Log.e(TAG, e.getMessage());
            }
            return token;
        }

        @Override
        protected void onPostExecute(String s) {
            super.onPostExecute(s);
            ((TextView) findViewById(R.id.token_value)).setText("Token Value: " + s);
        }
    }
}

https://code.google.com/p/google-api-java-client/wiki/Setup