How do you kill a Thread in Java?

Generally you don't..

You ask it to interrupt whatever it is doing using Thread.interrupt() (javadoc link)

A good explanation of why is in the javadoc here (java technote link)

See this thread by Sun on why they deprecated Thread.stop(). It goes into detail about why this was a bad method and what should be done to safely stop threads in general.

The way they recommend is to use a shared variable as a flag which asks the background thread to stop. This variable can then be set by a different object requesting the thread terminate.

In Java threads are not killed, but the stopping of a thread is done in a cooperative way. The thread is asked to terminate and the thread can then shutdown gracefully.

Often a volatile boolean field is used which the thread periodically checks and terminates when it is set to the corresponding value.

I would not use a boolean to check whether the thread should terminate. If you use volatile as a field modifier, this will work reliable, but if your code becomes more complex, for instead uses other blocking methods inside the while loop, it might happen, that your code will not terminate at all or at least takes longer as you might want.

Certain blocking library methods support interruption.

Every thread has already a boolean flag interrupted status and you should make use of it. It can be implemented like this:

public void run() {
   try {
      while (!interrupted()) {
         // ...
      }
   } catch (InterruptedException consumed)
      /* Allow thread to exit */
   }
}

public void cancel() { interrupt(); }

Source code adapted from Java Concurrency in Practice. Since the cancel() method is public you can let another thread invoke this method as you wanted.