A base class object should have a virtual destructor, when it is necessary for the base class to do its own cleanup. This is to say, if you have allocated resources in the base class it is necessary for the base class to cleanup, by declaring its destructor virtual you guarantee that this cleanup will be done (assuming you wrote the cleanup correctly).
In general, methods can be defined virtual in a base class, this will allow derived classes to override the virtual methods, implementing their own derived specific implementation. I find this is most clearly demonstrated with a simple example. Say we have a base class 'Shape', now all derived classes may be required to have the ability to draw. The 'Shape' object will not know how to draw classes derived from it, so in the 'Shape' class we define a virtual draw function. ie (virtual void draw();). Now in each base class we can override this function, implementing specific drawing code (ie. a square is drawn differently from a circle).
