This is the sort of thing I usually use for such purposes. Note this is recursive and therefore will search subdirectories also. :-)

#!/usr/bin/perl -w
# Recurse directories to find .txt files

use strict;
use File::Find;

my $file = '';
my $dir  = '';

@ARGV = qw(.) unless @ARGV; # current dir unless otherwise specified

$dir = shift @ARGV;

sub process_file {
           return unless -f;        #skip directories
           $file = $_;
           if ($file =~ m/\.(txt)/si) {
               # do stuff here
           } 
}

find(\&process_file, $dir);
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HTH,

Update: Deleted a spurious line from the code. The original is from an example on recursive editing, and I stripped some (but not all) of the non-relevant code. Oops. ;-)

planetscape gave the complete answer, here's a simpler option without recursiveness, using glob:

for my $filename (glob("*.txt")) {
  next if (!-f $filename);
  open(my $fh,"<",$filename) or die "Can't open $filename for reading"
+;
  #...process file
}
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 #this decode utf8 routine is used so filenames with extended 
   # ascii characters (unicode) in filenames, will work properly 
   use Encode;
   opendir my $dh, $path or warn "Error: $!";
   my @files = grep !/^\.\.?$/, readdir $dh;
   closedir $dh;
   # @files = map{ "$path/".$_ } sort @files; 
   #$_ = decode( 'utf8', $_ ) for ( @files ); 
   @files = map { decode( 'utf8', "$path/".$_  ) } sort @files;
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