Going to home screen programmatically

One line solution

moveTaskToBack(true); //activity.moveTaskToBack(true);

it will behave as Home Button is pressed

You can do this through an Intent.

Intent startMain = new Intent(Intent.ACTION_MAIN);
startMain.addCategory(Intent.CATEGORY_HOME);
startMain.setFlags(Intent.FLAG_ACTIVITY_NEW_TASK);
startActivity(startMain);

This Intent will start the launcher application that the user has defined. Be careful with this because this will look like your application crashed if the user does not expect this.

If you want this to build an exit button from your app please read this article on exit Buttons in Android