As 3dan notes, this question has been asked and answered many times. But just for fun, here's a quick (tested) solution that takes a different approach from that of tcf22. This leaves a hash (%counts) with all the results available for later processing. (tcf22's approach could be adjusted to do that also.)

#!/usr/bin/perl -w
use strict;

my @array_1 = qw/A B/;
my @array_2 = qw/A B C D A D B A C/;

my %check_1 = map { $_ => 1 } @array_1;
my %counts;
map { $counts{$_}++ if $check_1{$_} } @array_2;

print "$_ : $counts{$_}\n" for keys %counts;
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Which results in:

    A : 3
    B : 2

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"Perl is a mess and that's good because the
problem space is also a mess." - Larry Wall