Check DBI, which should be your #1 reference in this matter :) The POD is fairly extensive and quite readable.

fetchrow_array is part of the statement handle object, not the database handle object (if I get it right)

If you change your code to the following, it'll probably works:

use warnings;
use DBI;
use DBD::mysql;
use CGI qw( :standard );
use CGI::Carp "fatalsToBrowser";
print header, start_html('SQL Must Work!'); # Great title ;)

my $dbh = DBI->connect("DBI:mysql:data:server","uname","pass") or
  die( "Could not make connection to database: $DBI::errstr" );

# Slightly altering this
my $sth = $dbh->prepare("SELECT Tab1, Tab2, Tab3 FROM UData");
$sth->execute;

# Using $sth, instead of $dbh
while (my @row = $sth->fetchrow_array ) {
   my ( $item0, $item1, $item2 ) = @row;

   if ($item0 >= $somevalue) {
      print br, "$item0"; 
   }
}

warn( $DBI::errstr ) if ( $DBI::err );
$dbh->disconnect();

print '<h2>All Done</h2>';
print end_html;
[download]

HTH