> (1) what are these brackets  for,

They indicate that you want an array of that type of object.

Contrast string  x and String []y.
x can only hold one string. y can hold n strings, where n is set when
you initialize the array.

> (2) do you ever put  anything inside  them,

Yes. just like when you initialize a single object, you need to
initialize arrays to a given size.

so, using the examples above,

x = new String(); // Allocates space  for 1 string and sets it to ""
y = new String[5]; // Allocates space for 5 strings. Does not set any
of them

> (3) do they only go after the word  "String",

No, you can have an array of any type, including the fundamental types
(int, char, double,...)

> and (4) are you supposed to have a space before the [] or not?

Coder's preference. The Java compiler ignores whitespace. Use whatever
looks good to you.