Referring here
A is a precompiled Java class (I also have the source file)
B is a Java class that I am authoring
B extends A.
How can logic be implemen
Class A should define the methods it's going to call (probably as abstract ones, and A should be an abstract class, per Paul Haahr's excellent guide); B can (in fact to be concrete MUST, if the method are abstract) override those methods. Now, calls to those methods from other methods in A, when happening in an instance of class B, go to B's overrides.
The overall design pattern is known as Template Method; the methods to be overridden are often called "hook methods", and the method performing the calls, the "organizing method".