You'll want to read perldata, perllol and perldsc (and maybe perlref and perlreftut for good measure :)

What you'll want to do is make a reference to a list of a list (of a list of a list ... etc.) For example:

my $array_1 = [ 1, 2, 3 ];   # 1d
my $array_2 = [ [1, 2, 3], [1, 2, 3], [1, 2, 3] ]; #2d
my $array_3 = [
  [ [1, 2, 3], [1, 2, 3], [1, 2, 3] ],
  [ [1, 2, 3], [1, 2, 3], [1, 2, 3] ],
  [ [1, 2, 3], [1, 2, 3], [1, 2, 3] ],
];                                           # 3d
... etc.
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which can be extended to however many dimensions you want. Using an array ref makes things easy because you can just pass $array_1, $array_2, $array_3 around as you would any ol' scalar. A specific cell in your n-dimensional array can be referenced as:

$array_1->[$x];
$array_2->[$x][$y];
$array_3->[$x][$y][$z];
... etc.
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Or, by "fixed dimensions" do you mean that your n-dimensional array is of a pre-determined size? In that case you can always use the old trick of storing everything in a single array with a pre-declared length and calculating every element's position (see your favorite algorithms/data structures book for details.)

update: I forgot to mention, if your n-dimensional array is sparsely populated, you might look into using a hash and "multidimensional array emulation".

my %array = ();
$array{$x1,$y1,$z1} = something;
$array{$x2,$y2,$z2} = something else;
...
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Obviously this is Terribly Bad if you need to loop around your array and, frankly, I've never had much use for this, but I thought I should bring it up in case it happens to work for you ...