Mostly people would do this with the shell, but if you want to write it by hand, it probably looks something like this.

open my $cmd, "-|", qw(ls -al) or die $!;
open my $file, ">", "filename" or die $!;
while(<$cmd>) {
   print $file $_
}
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If you're interested in stdout as well as stderr, IPC::System::Simple might have a role to play.