I agree this is a bad example to use polymorphism in but you might as well try it.

First, I need an abstract method. Is it just sub foo {}; or sub foo; or what? Or should I leave the declaration away altogether?

I usually croak in abstract methods, in hopes they are always overloaded.

sub process_input
{
    croak "Cannot use an abstract method;
}
[download]

Second, but most important, now that the switch is gone, how do I go about from user input $foo to a certain subclass foo method? Drawing a blank here.

You can maybe use a Factory design pattern, or have a sub choose the object. This is basically another switch statement :P. Or maybe you can use a dispatch table like the one shown above.

Third, sharing code between B and C is more difficult. Formerly, when everything was in one package, I just had a sub for the common code. How do I handle that now that they are in different classes?

Hmmm.. you could have C be a subclass of B...