You can generally connect to a remote Oracle database in this manner:

sub db_connect_remote {
  my ($sid,$user,$password) = @_;
  my $oracle_home = 'location_of_oracle_on_your_system';
# /orasw/app/oracle/product/10.0.2 on my system
  $user = $user ? $user : 'some_default_value';
  $password = $password ? $password : 'some_default_value';
  $sid = $sid ? $sid : 'some_default_value';
  
  unless (opendir(ORA_HOME,$oracle_home)) {
    print "Cannot locate ORACLE_HOME (expected $oracle_home)\n";
    return 0;
  }
  $ENV{'ORACLE_HOME'} = $oracle_home;
  my $dbh = DBI->connect("dbi:Oracle:$sid", 
               $user, $password, { RaiseError => 1, AutoCommit => 0 })
      or die "Can't connect to Oracle $sid: $DBI::errstr";
  return $dbh;
}
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Of course, this depends on an entry for that SID in your local tnsnames.ora file -- but basically, if you can log in via SQLNet from that host, you can probably log in via the DBI in this fashion.