You're on the right track already, except that variable names in Perl are prefixed by a sigil - $ is the sigil for a single value, while @ is the sigil for an array/a list, and % is the sigil for a hash ("associative array" in awk).

For a start, I'd just convert the stuff behind the cat invocation verbatim which is the trickier part:

use strict;

# Read from standard input
while (<>) {
    s/;/\n/g; # this is just like sed
    s/:/\n/g; # this is just like sed

    # Now, split the input line on newlines, like awk will do:
    my @pages = split /\n/;

    for my $page (@pages) {
        # I'm using qq{...} instead of double quotes (")
        # so I don't have to escape the stuff in ugly ways
        print qq{<a href="http://mysite.net/$page">$page</a>\n};
    };
};
[download]

To convert the two verbatim sed commands and the awk command into one thing that just takes everything that is delimited by ; or : and prints out a HTML link to it, I'd rewrite the loop as follows:

use strict;

# Read from standard input
while (<>) {

    # Remove the newline at the end of $_
    chomp;

    # Split the input line on ":" or ";":
    my @pages = split /[:;]/;

    for my $page (@pages) {
        # I'm using qq{...} instead of double quotes (")
        # so I don't have to escape the stuff in ugly ways
        print qq{<a href="http://mysite.net/$page">$page</a>\n};
    };
};
[download]

Update: Replaced my erroneous use of $1 with $page, which is the correct variable to use. Thanks, johngg!