This error will occur when java tries to access an object which has not yet been instantiated. So, for example, if you declare a field
you must make sure to say
js = new Joystick(0);
otherwise, a NullPointerException will be thrown.
The more low-level reason behind this error is that behind the scenes, objects are essentially memory addresses. When declared and not instantiated, the object "points to" the memory address 0 (i.e. null). Unfortunately (or perhaps fortunately), attempts to access data stored at 0 are illegal (the java police will arrest you). So an address must be assigned. The keyword new does just that: it allocates a space in memory and can be used to store it in an object. If you know someone who knows C or C++, they might be able to explain this better.
How to Fix It
This is an easy but tedious fix. Make sure that every time you use a variable, it has been instantiated previously. It is actually pretty easy to forget to do this with class variables, so make sure that in a method that always run (such as the init methods), each variable is initialized. Good luck...