This would be a very simple implementation:
public void onClick(View v) {
    new Thread(new Runnable() {
        public void run() {
            try {
                URL url = new URL("http://");
                HttpURLConnection conn = (HttpURLConnection) url.openConnection();
                try {
                    conn.setReadTimeout(10000 /* milliseconds */);
                    conn.setConnectTimeout(15000 /* milliseconds */);
                    conn.setRequestMethod("GET");
                    conn.setDoInput(true);
                    conn.connect();
                } finally {
                    conn.disconnect();
                }
            } catch (IOException exception) {
                throw new RuntimeException(exception);
            }
        }
    }).start();
}
If you want to do more (such as handling a response from the webpage), read the documentation.