If I structure a solution as a c, java, or BASIC programmer might:

my %word_list = ( bat=> 0, cat=> 0, eat=> 0, fat=> 0 );
my @words = qw( bat bat dat fat eat eat eat fat );
my $word;

foreach $word (@words){
   if(exists $word_list{$word}){
      $word_list{$word}= $word_list{$word} + 1; 
   }
   else{
      $word_list{$word} = 1;
   }
}

foreach $word (sort keys %word_list) {
   print "$word: $word_list{$word}\n";
}
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If I want a perlish solution I would write:

%word_list = ( bat=> 0, cat=> 0, eat=> 0, fat=> 0 );
my @words = qw( bat bat dat fat eat eat eat fat );
my $word;
foreach $word (@words){
   $word_list{$word}++;
}

foreach $word (sort keys %word_list) {
   print "$word: $word_list{$word}\n";
}
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If don't need a the original word_list for displaying words that were not matched (word count is 0) but want only the counts of the words that occur in @words then an empty %word_list.

my %word_List = ( );
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Using a hash and increment to count things is a fundamental technique to master early in your perl walk.

RBL