#!/usr/local/bin/perl -w

use strict;
use POSIX; # added after observing BrowserUK's code

my (%schedule, $backup_type);

my $today = strftime( '%A', localtime ); # changed after observing BrowserUK's code

while (my $line = <DATA>) {
  chomp $line;
  my $count = 0 ;
  if ($line =~ /schedule:\s+(\w+)/i){
    my $count++;
    $backup_type = $1;
  }
  if ( $line =~ /(\w+day)\s+(\d{2}\:\d{2}\:\d{2})/i ){
    $schedule{$1} = {
      'backup_type' => $backup_type, 
      'time' => $2
      };
  }
}

printf "Today is %s and the backup type is %s to begin at %s\n",
  $today, $schedule{$today}->{'backup_type'}, $schedule{$today}->{'time'};

__DATA__
...etc