The difference between the "beginner way" and a presumably more advanced technique is merely style. As long as you continue to produce working code, your skill will improve. With experience comes an ability to write less code to get the same job done. Fewer lines of code means less code to debug, which can reduce the likelihood of producing defective code. This artifact is difficult to explain to employers who judge performance on lines of code produced. Alas.

Here's some tips that could make your program "better", though what that means in practice is actually highly subjective.

      my($day,$month,$year) = (localtime)[3,4,5];
      $month = $month + 1;
      $year = $year + 1900;
      my $date = "$month\/$day\/$year";
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This four line chunk could be reduced into something like this:

      my (@time) = (localtime)[4,3,5];
      my ($date) = sprintf ("%d/%02d/%02d", $time[0]+1900, $time[1]+1,
+ $time[2]);

      # Or if you don't care about formatting:
      my ($date) = join ('/', $time[0]+1900, $time[1]+1, $time[2]);

      # Or if you want to combine with your print, which would
      # avoid having to declare $date:
      printf GRAVE ("# consigned to the graveyard on %d/%d/%d\n",
                    $date[0]+1900,
                    $date[1]+1,
                    $date[2]);
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sprintf allows you to convert a list of items into a string, with formatting. It's a little hairy to use at first, but with a little practice it comes in quite handy. join() allows you to put things together on the double, but doesn't offer much flexibility.

      while(<FILE>) {
          push @output, $_;
      }
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You will notice here that you are taking something from one array (<FILE>) and putting it into another (@output). Why not do it in one shot?      @output = <FILE>; BTW, it would seem that your program inserts things into the GRAVE double-spaced. You're not removing the "\n" from the input stream FILE, so it's still there when you go and write into GRAVE with "$line\n"...

An interesting read is in the back of the "Camel Book" where they compare Program Efficiency vs. Programmer Efficiency and how you can choose to optimize around either. The 'Camel Book' is virtually essential to developing a full understanding of the Perl language, as there are few with the same depth and scope.