Create one Broadcast Receiver for that and register it in manifest file.

First create a new class NetworkStateReceiver and extend BroadcastReceiver.

public class NetworkStateReceiver extends BroadcastReceiver {
    public void onReceive(Context context, Intent intent) {
     Log.d("app","Network connectivity change");
     if(intent.getExtras()!=null) {
        NetworkInfo ni=(NetworkInfo) intent.getExtras().get(ConnectivityManager.EXTRA_NETWORK_INFO);
        if(ni!=null && ni.getState()==NetworkInfo.State.CONNECTED) {
            Log.i("app","Network "+ni.getTypeName()+" connected");
        }
     }
     if(intent.getExtras().getBoolean(ConnectivityManager.EXTRA_NO_CONNECTIVITY,Boolean.FALSE)) {
            Log.d("app","There's no network connectivity");
     }
   }
}

Put this code in your AndroidManifest.xml under the "application" element:

<receiver android:name=".NetworkStateReceiver">
   <intent-filter>
      <action android:name="android.net.conn.CONNECTIVITY_CHANGE" />
   </intent-filter>
</receiver>

And add this permission

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

EDIT

This code just detects connectivity change but cannot tell whether the network it is connected to has a internet access. Use this method to check that -

public static boolean hasActiveInternetConnection(Context context) {
    if (isNetworkAvailable(context)) {
        try {
            HttpURLConnection urlc = (HttpURLConnection) (new URL("http://www.google.com").openConnection());
            urlc.setRequestProperty("User-Agent", "Test");
            urlc.setRequestProperty("Connection", "close");
            urlc.setConnectTimeout(1500); 
            urlc.connect();
            return (urlc.getResponseCode() == 200);
        } catch (IOException e) {
        Log.e(LOG_TAG, "Error checking internet connection", e);
        }
    } else {
    Log.d(LOG_TAG, "No network available!");
    }
    return false;
}

The code from Chirag Raval above certainly works. The trouble is that the listener will get invoked even when the application is not running in foreground.

IMHO, the better approach is to register / unregister the receiver in the onResume() / onPause() methods of all your application activities. This code should do it:

private final NetworkStateReceiver stateReceiver = new NetworkStateReceiver();

@Override
protected void onResume() {
    super.onResume();
    IntentFilter filter = new IntentFilter();
    filter.addAction("android.net.conn.CONNECTIVITY_CHANGE");
    registerReceiver(stateReceiver, filter);
}

@Override
protected void onPause() {
    super.onPause();
    unregisterReceiver(stateReceiver);
}

Obviously, remove the registration from AndroidManifest.xml file.

Using this solution, the receiver will be called also when switching between activities of your application (assuming you are closing them). In such a case, use a static flag (being shared between all your activities) like in the example below (called online):

public class NetworkStateReceiver extends BroadcastReceiver {

    private static boolean online = true;  // we expect the app being online when starting

    public static final String TAG = NetworkStateReceiver.class.getSimpleName();

    public void onReceive(Context context, Intent intent) {
        Log.d(TAG,"Network connectivity change");
        ConnectivityManager manager = (ConnectivityManager) context.getSystemService(Context.CONNECTIVITY_SERVICE);
        NetworkInfo ni = manager.getActiveNetworkInfo();
        if (ni == null || ni.getState() != NetworkInfo.State.CONNECTED) {
            Log.d(TAG,"There's no network connectivity");
            if (online) // don't show the message if already offline
                Toast.makeText(context, R.string.noInternet, Toast.LENGTH_SHORT).show();
            online = false;
        } else {
            Log.d(TAG,"Network "+ni.getTypeName()+" connected");
            if (!online)  // don't show the message if already online
                Toast.makeText(context, R.string.backOnline, Toast.LENGTH_SHORT).show();
            online = true;
        }
    }
}

If starting your app when being offline, the Toast message will appear; otherwise it appears only when losing / re-establishing the connection .