For example:

String: now is the time
Regex: /\stime/

Result: now is the time
Matched: Yes
[download]

might be uninformative to the newcomer who hasn't yet groked much about regexen (and, specifically, about the need to use capturing parens in your program to obtain appropriate feedback). OTOH, of course, it works splendidly for this (in which our presumed newcomer has come to understand captures, even if s/he can't follow your code):

String: now time
Regex: /now\s(time)/

Result: now time
Matched: Yes
Captures: [#1: 'time']
[download]

So, Good to go! for those who have at least some of the basics... but:

My bad! See alexm's correction, below.
String: fred same joe time
Regex: ?time?
The regex must be a valid match or a substitute expression.

String: |time|
Regex: |time|
The regex must be a valid match or a substitute expression.

String: fred same time
Regex: ~time~
The regex must be a valid match or a substitute expression.

String: fred same time
Regex: !time!
The regex must be a valid match or a substitute expression.

Perhaps a brief addition to the use_instruction (line 10) specifying the use of /.../ as the acceptable regex delimiter for input to this script (or re-coding to accept the usual alternatives?) and a bit of clarification about the output would make your script an even more valuable tool.

Regex: ?time?
...
Regex: |time|
...
Regex: ~time~
...
Regex: !time!
[download]

You must add the m prefix unless you use the slash; it works the same way it does on Perl:

String: fred same joe time
Regex: m?time?

Result: fred same joe time
Matched: Yes

String: fred same joe time
Regex: m~time~

Result: fred same joe time
Matched: Yes

String: fred same joe time
Regex: m|time|

Result: fred same joe time
Matched: Yes

String: fred same joe time
Regex: m!time!

Result: fred same joe time
Matched: Yes
[download]

See also this regex thingy (external link).

#!usr/bin/perl

$my_string = "";
$my_regx = "";

 # This program tests regular expressions against a match.

 if ($my_string =~ /$my_regx/x) 

    print "Matched: "  . "\"" .  $&  . "\"" . "\n";       # print matc
+h
    print "Before match: "  . "\"" .  $`  . "\"" .  "\n"; # print data
+ before match
    print "After match: " . "\"" . $' . "\"" . "\n";      # print data
+ after match

}else {
    # do nothing
} # end if
    
  print "Rockstar Programming Inc. All Rights Reserved\n";
[download]

There are a few things here that could use a little tidying. First off, the mandatory mantra: Always use strictures (use strict; use warnings; - see The strictures, according to Seuss).

Of more immediate benefit: if you find you need to include double quote character in a string use qq for quoting instead of " (see perlop's Quote and Quote-like Operators). For example your print statements become:

    print qq{Matched: "$&"\n};       # print match
    print qq~Before match: "$`"\n~; # print data before match
    print qq|After match: "$'"\n|;      # print data after match
[download]

although you may wish to use a here-doc instead (look for here-doc in the same docs mentioned above):

    print <<STUFF;
Matched: "$&"
Before match: "$`"
After match: "$'"
STUFF
[download]

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Perl reduces RSI - it saves typing