How do I prevent the modification of a private field in a class?

If you can use a List instead of an array, Collections provides an unmodifiable list:

public List<String> getList() {
    return Collections.unmodifiableList(list);
}

You must return a copy of your array.

public String[] getArr() {
  return arr == null ? null : Arrays.copyOf(arr, arr.length);
}