The easiest method is to use the toArray(IntFunction<A[]> generator) method with an array constructor reference. This is suggested in the API documentation for the method.
String[] stringArray = stringStream.toArray(String[]::new);
What it does is find a method that takes in an integer (the size) as argument, and returns a String[], which is exactly what (one of the overloads of) new String[] does.
You could also write your own IntFunction:
Stream<String> stringStream = ...;
String[] stringArray = stringStream.toArray(size -> new String[size]);
The purpose of the IntFunction<A[]> generator is to convert an integer, the size of the array, to a new array.
Example code:
Stream<String> stringStream = Stream.of("a", "b", "c");
String[] stringArray = stringStream.toArray(size -> new String[size]);
Arrays.stream(stringArray).forEach(System.out::println);
Prints:
a
b
c