How can I do something 0.5 seconds after text changed in my EditText control?

Use:

editText.addTextChangedListener(
    new TextWatcher() {
        @Override public void onTextChanged(CharSequence s, int start, int before, int count) { }
        @Override public void beforeTextChanged(CharSequence s, int start, int count, int after) { }

        private Timer timer = new Timer();
        private final long DELAY = 1000; // Milliseconds

        @Override
        public void afterTextChanged(final Editable s) {
            timer.cancel();
            timer = new Timer();
            timer.schedule(
                new TimerTask() {
                    @Override
                    public void run() {
                        // TODO: Do what you need here (refresh list).
                        // You will probably need to use
                        // runOnUiThread(Runnable action) for some
                        // specific actions (e.g., manipulating views).
                    }
                },
                DELAY
            );
        }
    }
);

The trick is in canceling and rescheduling Timer each time, when text in EditText gets changed.

For how long to set the delay, see this post.