For example:

my @array1 = qw(a b c d e);
my @array2 = qw(a c d e b);

# assign numbers and create lookup table
my $i;
my %pos1 = map { $_ => ++$i } @array1;

# lookup items of array2
my @pos2 = map $pos1{$_}, @array2;

print "@pos2\n";  # 1 3 4 5 2
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The hash %pos1 maps strings to numbers, i.e. you can lookup the number associated with for example "a" by writing $pos1{a}, which would give 1 here.

(If items can occur more than once in array1 (i.e. not unique), you'd have to define how to deal with that case...)