java.utilパッケージ - Calendarクラスを使用します。
サンプルソースコード
final Calendar calendar = Calendar.getInstance();
final int year = calendar.get(Calendar.YEAR);
final int month = calendar.get(Calendar.MONTH);
final int day = calendar.get(Calendar.DAY_OF_MONTH);
final int hour = calendar.get(Calendar.HOUR_OF_DAY);
final int minute = calendar.get(Calendar.MINUTE);
final int second = calendar.get(Calendar.SECOND);
final int ms = calendar.get(Calendar.MILLISECOND);
Log.v("year/month/day hour:minute:second",
year + "/" + (month + 1) + "/" + day + "/" + " " +
hour + ":" + minute + ":" + second + "." + ms);
参考ページ