Have a look at $INPUT_RECORD_SEPARATOR or $/ in perlvar for how to read your data file record by record. Have a look at split to break each record into fields and perldsc and push for building an array of arrays. Then think how you would iterate over all of the elements; perhaps a nested loop?

Have a go at putting this all together then come back to the Monastery with any problems you are having with your code.

use 5.010;
my @s;
while (<DATA>) {
    my @e = split;
    $s[$_] += $e[$_] for 0 .. $#e;
}
say "@s";
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You could also add up the elements on each line with sum from List::Util, so the code above would become:

use 5.010;
use List::Util qw(sum);
my @s;
push @s, sum( split ) while <DATA>
say "@s";
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;; Presented with just about as much Perl as the OP . . .
(ns sumcols
  (:use [clojure.contrib.str-utils :only (re-split)])
  (:use [clojure.contrib.duck-streams :only (read-lines)]))

(defn sumline [acc line]
  (loop [a acc l (map #(Float. %) (re-split #"\s+" line)) idx 0]
    (if (empty? l) a
      (recur (assoc a idx (+ (get a idx 0) (first l))) (rest l) (inc i
+dx)))))

(defn sumcols [filename]
  (loop [acc {} lines (filter #(> (count %) 0) (read-lines filename))]
    (if (empty? lines) (vals acc)
      (recur (sumline acc (first lines)) (rest lines)))))

(println (sumcols (first *command-line-args*)))
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use strict;

my @data;
open(INPUT,'<',"monks.dat") or die("Can't open file");
while (<INPUT>) {
    chomp;
    my @newdata = split(/ +/);
    for my $index (0 .. $#newdata) {
        $data[$index] += $newdata[$index];
    }
}
close(INPUT);
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Why not use a spreadsheet? Import the data as fixed width or specify a space as the delimiter. Are you doing this to learn Perl?

By the way: __DATA__ needs to have 2 underscores in front and back to work in a perl script, it looks like you only have one.