It's generally good form to include specific examples of what strings you want to transform and what you want the results to be (see How (Not) To Ask A Question). The documentation for how to use regular expressions can be found at perlre, with a tutorial at perlretut. While it is certainly possible to do this in a one-liner, given your stated experience level, you probably want to open the file (I/O Operators), make changes and then write the info out. And, as ikegami states, I think that \$ in your regex looks hinky.

You'll probably want something like:

#!/usr/bin/perl
use strict;
use warnings;
use Date::Format;

my ($input_file, $output_file) = @ARGV;

my $date = time2str("%Y-%m-%d", time);
#print "\n\n$date\n\n";
## works

open my $input, '<', $input_file or die "Open failure on $input_file: 
+$!";
my @contents = ();
while (defined (my $line = <$input>)) {
    $line =~ s/(\d\d\d\d-\d\d-\d\d)(-[a-z_]{5,30}\.zip)/$date$2/;
    push @contents, $line;
}
close $input;

open my $output, '>', $output_file or die "Open failure on $output_fil
+e: $!";
foreach my $line (@contents) {
    print $output $line;
}
close $output;
[download]

This code could certainly be improved, but it should be sufficiently step-by-step to provide a good idea of how to proceed. The script as written should be called with

> perl script.pl infile outfile

The input and output file names can be the same for in-place edits.