Keep storing in array until there is input from users without knowing number of elements at first?

You can use ArrayList or HashSet (if uniqueness is required). Collections can grow dynamically as required. If you need array as a type, accept user data into Arraylist (or any other collection) and then create array from collection using toArray

Java has data structures that already do this for you (e.g. ArrayList). But if you really need to implement it yourself, then a standard method would be to store the number of elements you've currently stored separately from the capacity of the array (i.e. its length).

For example for a String array that starts at size 10 and doubles in size when it is full:

String[] array = new String[10];
int size = 0;

private add(String item) {
    if (size == array.length)
        array = Arrays.copyOf(array, array.length * 2);
    array[size++] = item;
}

If performance isn't important then you can expand on every element and avoid storing the size (as it's always equal to the array's length):

array = Arrays.copyOf(array, array.length + 1);
array[array.length - 1] = item;