The simplest way is a one-liner:

  perl -i.bak -pe 's/hello/goodbye/gi' file1 file2 ...
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You are reading the file and modifying an in-memory string, but not attempting to write that string back out. I would do this:

  use Fcntl qw(:seek);

  open (FOO, "+<$foo") or die "Can't open $foo: $!";
  my $slurp = join '', <FOO>;
  $slurp =~ s/hello/goodbye/sgi;
  seek FOO, 0, SEEK_SET;
  print FOO $slurp;
  truncate FOO, tell FOO;
  close FOO;
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Update: Added the truncate call for cases where the modified file contents are shorter than the original. Oops.