sub s1 {
  my $sub=shift;  # get it!
  # you may want to add checks => perldoc -f ref.
  print "s1";
  $sub->();       # execute it!
}
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Indeed they gave you a good suggestion: this is the best way to do what you say you want to do.

You could even make it default to the original s2 if the argument isn't supplied:

sub s1 {
  my $sub = shift || \&s2;
  print "s1";
  $sub->();
}
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This didn't work. It is still using the wrong s2.

If I do it that way, how do i supply arguments to $sub in s1? For example the s2 subroutine takes in 2 parameters. How do I put those parameters into the $sub once I am in s1?

I was thinking of something like:

$sub->($value1, $value2);
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But that doesn't work...

It does work. Well, it should. What are you really trying to do? It's hard to tell without seeing the rest of your code.

TT.pm (also taking into account ikegami's very good suggestion)

# -*- Perl -*-

use strict;
use warnings;

package TT;

use base 'Exporter';
our @EXPORT = qw/s1/;

sub s1 {
    my $sub = shift || \&s2;
    $sub->(qw/foo bar/);
}

sub s2 {
    print "Default s2\n";
    print "Args: @_\n";
}

1;


__END__
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testTT.pl

#!/usr/bin/perl

use strict;
use warnings;
use TT;

# s1 with no args;
s1;

print "\n";

# s1 with explicit code passed in;
s1 sub {
    local $\="\n";
    print "Customized s2";
    print "Args:";
    print for @_;
};


__END__
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(Try it yourself!) output:

Default s2
Args: foo bar

Customized s2
Args:
foo
bar
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Incidentally, perldoc perlsub and perldoc perlref would help.