A line by line critique:

use Net::FTP;

# You should 'use strict' if the final script is
# going to be any longer than 5 or 10 lines,
# which would make the next line 'my $ftp = ...'.
# Also, according to the Net::FTP docs, connect
# errors are reported in $@, not $!
$ftp = Net::FTP->new("$host", debug => 1) or die "Host:   $!";

# Error messages after new are reported in the
# message() method ($ftp->message, and don't put it inside
# quotes since methods won't get interpolated inside
# quotes). This method is documented in Net::Cmd, which
# Net::FTP inherits from.
# Are $user and $pass set to anything?
$ftp->login($user,$pass) or die "Login:    $!";

# Same comment as above.
$ftp->cwd() or die "Dir: $!";

# Are $file and $dir set to anything?
# Does $dir exist on the local system?
# Does $file exist in the current directory
# on the remote system?
# Is there a permission problem?
# And you don't need to backwhack the "/"
$ftp->get("$file","$dir\/$file") or die "File:    $!";
$ftp->quit;
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Also, in general, you don't need to put quotes around just a single variable, e.g. "$file", though some people consider it a matter of preference.
And again, Use strict and warnings :-)