I can't see how to enter that with my $subst = <STDIN>;

True, it won't work this way ... it might be feasible with a slight syntax tweak and one further step to process it ... assumes that you know ... you might need some newline characters to be reprocessed

As long as you can get  \nything into a scalar, you can search/replace with it, and a statement like
    my $subst = <STDIN>;
is perfectly adequate to capture any sequence with a literal backslash in it:

c:\@Work\Perl>perl -wMstrict -e
"print 'enter a string: ';
 my $string = <STDIN>;
 chomp $string;
 print qq{'$string' \n};
"
enter a string: )\n(
')\n('
[download]

(Caveat: Actually, I can only test this under Windoze; there may be OSen that mung backslashes in situations like this.)

Once you have captured a string with a backslash, you can use it for search/replace straightforwardly:

c:\@Work\Perl>perl -wMstrict -le
"printf 'enter search regex: ';
 my $search = <STDIN>;
 chomp $search;
 ;;
 printf 'enter replacement string: ';
 my $replace = <STDIN>;
 chomp $replace;
 ;;
 print qq{doing s/$search/$replace/};
 ;;
 my $s = qq{as\ngh\njk};
 printf qq{%*s: '$s' \n}, 7, 'initial';
 ;;
 my @regex = (
   { lh => $search, rh => $replace, },
   );
 ;;
 for my $hr_s (@regex) {
   $s =~ s[ (?-x)$hr_s->{lh}]{ qq{qq{$hr_s->{rh}}} }xmsgee;
   }
 ;;
 printf qq{%*s: '$s' \n}, 7, 'final';
"
enter search regex: \n
enter replacement string: __\n__
doing s/\n/__\n__/
initial: 'as
gh
jk'
  final: 'as__
__gh__
__jk'
[download]

(This is essentially the example code from below.)