First you need to define a LocationListener to handle location changes.

int LOCATION_REFRESH_TIME = 15000; // 15 seconds to update
int LOCATION_REFRESH_DISTANCE = 500; // 500 meters to update

....

private final LocationListener mLocationListener = new LocationListener() {
    @Override
    public void onLocationChanged(final Location location) {
        //your code here
    }
};

Then get the LocationManager and ask for location updates

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

    mLocationManager = (LocationManager) getSystemService(LOCATION_SERVICE);

    mLocationManager.requestLocationUpdates(LocationManager.GPS_PROVIDER, LOCATION_REFRESH_TIME,
            LOCATION_REFRESH_DISTANCE, mLocationListener);
}

And finally make sure that you have added the permission on the Manifest,

For using only network based location use this one

<uses-permission android:name="android.permission.ACCESS_COARSE_LOCATION"/>

For GPS based location, this one

<uses-permission android:name="android.permission.ACCESS_FINE_LOCATION"/>

I have written detailed tutorial covering this topic here on demonuts.com.You can find more description here and also you can download whole demo source code for better understanding.

First of all, put this in gradle file

 compile 'com.google.android.gms:play-services:9.0.2'

then implement necessary interfaces

public class MainActivity  extends BaseActivitiy implements GoogleApiClient.ConnectionCallbacks, GoogleApiClient.OnConnectionFailedListener, com.google.android.gms.location.LocationListener

declare instances

  private GoogleApiClient mGoogleApiClient;
  private Location mLocation;
  private LocationManager locationManager;
  private LocationRequest mLocationRequest;

put this in onCreate()

 mGoogleApiClient = new GoogleApiClient.Builder(this)
                .addConnectionCallbacks(this)
                .addOnConnectionFailedListener(this)
                .addApi(LocationServices.API)
                .build();
        locationManager = (LocationManager) getSystemService(Context.LOCATION_SERVICE);

At last, override necessary methods

 @Override
    public void onConnected(Bundle bundle) {
        if (ActivityCompat.checkSelfPermission(this, Manifest.permission.ACCESS_FINE_LOCATION) != PackageManager.PERMISSION_GRANTED && ActivityCompat.checkSelfPermission(this, Manifest.permission.ACCESS_COARSE_LOCATION) != PackageManager.PERMISSION_GRANTED) {
            // TODO: Consider calling
            //    ActivityCompat#requestPermissions
            // here to request the missing permissions, and then overriding
            //   public void onRequestPermissionsResult(int requestCode, String[] permissions,
            //                                          int[] grantResults)
            // to handle the case where the user grants the permission. See the documentation
            // for ActivityCompat#requestPermissions for more details.
            return;
        } startLocationUpdates();
        mLocation = LocationServices.FusedLocationApi.getLastLocation(mGoogleApiClient);
        if(mLocation == null){
            startLocationUpdates();
        }
        if (mLocation != null) {
            double latitude = mLocation.getLatitude();
            double longitude = mLocation.getLongitude();
        } else {
            // Toast.makeText(this, "Location not Detected", Toast.LENGTH_SHORT).show();
        }
    }

    protected void startLocationUpdates() {
        // Create the location request
        mLocationRequest = LocationRequest.create()
                .setPriority(LocationRequest.PRIORITY_HIGH_ACCURACY)
                .setInterval(UPDATE_INTERVAL)
                .setFastestInterval(FASTEST_INTERVAL);
        // Request location updates
        if (ActivityCompat.checkSelfPermission(this, Manifest.permission.ACCESS_FINE_LOCATION) != PackageManager.PERMISSION_GRANTED && ActivityCompat.checkSelfPermission(this, Manifest.permission.ACCESS_COARSE_LOCATION) != PackageManager.PERMISSION_GRANTED) {
            // TODO: Consider calling
            //    ActivityCompat#requestPermissions
            // here to request the missing permissions, and then overriding
            //   public void onRequestPermissionsResult(int requestCode, String[] permissions,
            //                                          int[] grantResults)
            // to handle the case where the user grants the permission. See the documentation
            // for ActivityCompat#requestPermissions for more details.
            return;
        }
        LocationServices.FusedLocationApi.requestLocationUpdates(mGoogleApiClient,
                mLocationRequest, this);
        Log.d("reque", "--->>>>");
    }

    @Override
    public void onConnectionSuspended(int i) {
        Log.i(TAG, "Connection Suspended");
        mGoogleApiClient.connect();
    }

    @Override
    public void onConnectionFailed(ConnectionResult connectionResult) {
        Log.i(TAG, "Connection failed. Error: " + connectionResult.getErrorCode());
    }

    @Override
    public void onStart() {
        super.onStart();
        mGoogleApiClient.connect();
    }

    @Override
    public void onStop() {
        super.onStop();
        if (mGoogleApiClient.isConnected()) {
            mGoogleApiClient.disconnect();
        }
    }
    @Override
    public void onLocationChanged(Location location) {

    }

Don't forget to start GPS in your device before running app.