Android: Background Stopwatch with Notification

Google has its clock app, which includes its stopwatch. I'm currently trying to create in my app a (count-up) timer, or you can call it a stopwatch, that will be able to run in the background, and when it runs in the background I want it to also show a notification, that displays the time it counts and a "Stop" button (all of this happens in google clock app (see here)). For the timer in my app, I'm using a Handler that posts a Runnable, which is posting itself. I'm writing my app in Java.

the code defining the 'timer' (Handler and Runnable):

Handler timerHandler = new Handler();
Runnable timerRunnable = new Runnable() {
    @Override
    public void run() {
        long millis = System.currentTimeMillis() - startTime;
        seconds = (millis / 1000) + PrefUtil.getTimerSecondsPassed();
        timerHandler.postDelayed(this, 500);
    }
};

my onPause function:

@Override
public void onPause() {
    super.onPause();

    if (timerState == TimerState.Running) {
        timerHandler.removeCallbacks(timerRunnable);
        //TODO: start background timer, show notification
    }

    PrefUtil.setTimerSecondsPassed(seconds);
    PrefUtil.setTimerState(timerState);
}

How can I implement the background service and the notification in my app?