Follow the steps mentioned below to get your location latitude and longitude

1) Create a class and name it LocationManger.java and impliment GoogleApiClient.ConnectionCallbacks, GoogleApiClient.OnConnectionFailedListener, LocationListener in the class

LocationManger.class

public class LocationManger implements
        GoogleApiClient.ConnectionCallbacks,
        GoogleApiClient.OnConnectionFailedListener,
        LocationListener {

    private final String TAG = "MyAwesomeApp";

    private GoogleApiClient mGoogleApiClient;

    private LocationRequest mLocationRequest;
    private static Context context;


    private LocationManger() {
    }

    private static LocationManger manager;

    public static LocationManger getInstance(Context _context) {
        if (manager == null) {
            manager = new LocationManger();
        }
        context = _context;
        return manager;
    }

    public void setUpLocation() {
        mGoogleApiClient = new GoogleApiClient.Builder(context)
                .addApi(LocationServices.API)
                .addConnectionCallbacks(this)
                .addOnConnectionFailedListener(this)
                .build();

        mGoogleApiClient.connect();
    }


    @Override
    public void onConnected(Bundle bundle) {
        if (servicesConnected()) {
            startPeriodicUpdates();
        }

    }

    private void startPeriodicUpdates() {
        mLocationRequest = LocationRequest.create();
        mLocationRequest.setPriority(LocationRequest.PRIORITY_HIGH_ACCURACY);
        mLocationRequest.setInterval(10000); // Update location every second

        LocationServices.FusedLocationApi.requestLocationUpdates(
                mGoogleApiClient, mLocationRequest, this);
    }

    /**
     * In response to a request to stop updates, send a request to
     * Location Services
     */
    private void stopPeriodicUpdates() {
        if (mGoogleApiClient.isConnected())
            System.out.println("destroy2");
        LocationServices.FusedLocationApi.removeLocationUpdates(mGoogleApiClient, this);
    }

    public void stopLocationUpdate() {
        stopPeriodicUpdates();
    }

    private boolean servicesConnected() {

        // Check that Google Play services is available
        int resultCode = GooglePlayServicesUtil.isGooglePlayServicesAvailable(context);
        // If Google Play services is available
        if (ConnectionResult.SUCCESS == resultCode) {
            // In debug mode, log the status
            // Continue
            return true;
            // Google Play services was not available for some reason
        } else {
            // Display an error dialog
            Dialog dialog = GooglePlayServicesUtil.getErrorDialog(resultCode, (Activity) context, 0);
            if (dialog != null) {
            }
            return false;
        }
    }


    @Override
    public void onConnectionSuspended(int i) {
        Log.i(TAG, "GoogleApiClient connection has been suspend");
    }

    @Override
    public void onConnectionFailed(ConnectionResult connectionResult) {
        Log.i(TAG, "GoogleApiClient connection has failed");
        ((LocationFound) context).locationFailed();
    }

    @Override
    public void onLocationChanged(Location location) {
        ((LocationFound) context).locationFound(location);
        stopLocationUpdate();                //stop location update. comment this line if you wish to get updated location latitude and longitude 


    }


    public interface LocationFound {
        public void locationFound(Location location);

        public void locationFailed();
    }

}

2) Now in your manin activity impliment LocationManger.LocationFound, this will help you to override locationFound and locationFaild method and call setUpLocation through LocationManger object.

MainActivity.class

public class MainActivity extends Activity implements LocationManger.LocationFound {

    private Location mLocation;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        LocationManger locationManger=LocationManger.getInstance(this);
        locationManger.setUpLocation();
    }

    @Override
    public boolean onCreateOptionsMenu(Menu menu) {
        // Inflate the menu; this adds items to the action bar if it is present.
        getMenuInflater().inflate(R.menu.menu_main, menu);
        return true;
    }

    @Override
    public boolean onOptionsItemSelected(MenuItem item) {
        // Handle action bar item clicks here. The action bar will
        // automatically handle clicks on the Home/Up button, so long
        // as you specify a parent activity in AndroidManifest.xml.
        int id = item.getItemId();

        //noinspection SimplifiableIfStatement
        if (id == R.id.action_settings) {
            return true;
        }

        return super.onOptionsItemSelected(item);
    }

    @Override
    public void locationFound(Location location) {
        //this.mLocation=location;
        Float speed=location.getSpeed();

        double latitude=location.getLatitude();
        double longitude=location.getLongitude();
        Toast.makeText(MainActivity.this, "latitude" + latitude + "longitude" + longitude, Toast.LENGTH_LONG).show(); //show your latitude and longitude on toast
    }

    @Override
    public void locationFailed() {

    }
}