Have a function create an object of the appropriate type.

use strict;
use warnings;

my $ob1 = My::File::Handler->new_handler('work.txt');
my $ob2 = My::File::Handler->new_handler('work.doc');

$ob1->write();
$ob2->write();

BEGIN {
    package My::File::Handler;
    sub new_handler {
       my ($class, $fn) = @_;
       my $ext = ...;  # built from $fn
       my $pkg = ...;  # built from $ext
       return $pkg->new($fn);
    }
    sub new{
        my ($class, $fn) = @_;
        return bless {}, $class;
    }
    sub write{
        my $self = shift;
        print $self->read;
    }
    sub read{
        die "Abstract";
    }
}

BEGIN {
    package My::File::Handler::txt;
    our @ISA = 'My::File::Handler';
    sub read{
        return __PACKAGE__;
    }
}

BEGIN {
    package My::File::Handler::doc;
    our @ISA = 'My::File::Handler';
    sub read{
        return __PACKAGE__;
    }
}
[download]

new_handler should probably be a method of another class.

I'd probably use Module::Pluggable to load the appropriate handler.