package Bar;

use base qw(CGI::Application);

sub useful_method {
  my $self = shift;

  # do something useful here
}

1;

package Foo;

use Base qw(Bar);
# By inheriting from Bar, we also inherit everything
# that Bar inherits, so you don't need to specifically
# mention CGI::Application in package Foo, since Bar
# deals with that for you

sub setup {
  my $self = shift;
  $self->run_modes(qw(runmode1 runmode2));
}

sub runmode1 {
  my $self = shift;

  my $results = $self->useful_method();

  ...
}

1;