Here are a few other pointers:

# Save some typing when you can!  Make your vars lexical where it make
+s sense.
my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) = localtime($
+tomorrows_time);

# Get the last two digits.  Much cleaner and faster
$year = substr($year,-2,2); 

# I like to use a variable to turn on/off the debug code
my $debug = 1; # somewhere near the top
print "Testing: $important_currencies{$abbrev}" if $debug;

# It's SO EASY to check for a zero in your divisor, so don't pass up t
+he free ride!  :) 
my $newrate;
if (!$second_currency) {
  print "HEY!  Don't divide!  You'll puke!\n";
}
else {
  $newrate = ($first_currency / $second_currency);
}
[download]

Here's my own version of the code. I liked the problem, so I played around with it a bit. Hopefully it has a few tasty tidbits that will help you out with future homework assignments.. erm, programming dilemmas. :) It looks like you put in some good thought and effort into your code, so I'm happy to help out!

my $tomorrows_time = time() + 86400;
my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) = localtime($
+tomorrows_time);
my $month_name=('JAN','FEB','MAR','APR','MAY','JUN','JUL','AUG','SEP',
+'OCT','NOV','DEC')[$mon];

$year = substr($year,-2,2);
$mday = sprintf("%02d", $mday);

my $date_stamp = "$mday-$month_name-$year";

my %conversions = (
    'AUD' => qq(USD),
    'CAD' => qq(USD),
    'DEM' => qq(USD),
    'FRF' => qq(USD GBP),
    'GBP' => qq(USD),
    'JPY' => qq(USD),
    'NZD' => qq(USD),
    'NLG' => qq(USD),
    'DEM' => qq(GBP),
    'EUR' => qq(USD GBP),
    'NZD' => qq(AUD),
    'ESP' => qq(GBP),
);

my %currencies = (
    'USD' => {
        'usd_equiv' => 1,
        'currency_per_usd' => 1,
    }
);

foreach (<DATA>) {
    my ($country,$abbrev,$usd_equiv,$currency_per_usd) = split /,/;
    next unless $usd_equiv && $currency_per_usd;
    $currencies{$abbrev}{usd_equiv} = $usd_equiv;
    $currencies{$abbrev}{currency_per_usd} = $currency_per_usd;
}


foreach my $currency (keys %conversions) {
    foreach my $comp_currency (split /\W+/, $conversions{$currency}) {
        print qq($currency,$comp_currency,$date_stamp,$date_stamp,);
        print sprintf("%f\n", ($currencies{$currency}{'usd_equiv'} / $
+currencies{$comp_currency}{'usd_equiv'}));
    }
}


__DATA__
Australian (Dollar),AUD,0.5295,1.8896
Canadian (Dollar),CAD,0.6295,1.5888
German (Mark),DEM,0.8794,1.1375
Spanish (Peseta),ESP,0.8794,1.1375
Euro,EUR,0.8794,1.1375
French (Franc),FRF,0.8794,1.1375
British (Pound),GBP,1.4316,0.6987
Hong Kong(Dollar),HKD,0.1282,7.7997
Italian (Lira),ITL,0.8794,1.1375
Japanese (Yen),JPY,0.007592,131.73
Dutch (Guilder),NLG,0.8794,1.1375
New Zealand (Dollar),NZD,0.4375,2.2883
[download]