Associating Post Category with Post using SQL

I am modifying Alex King’s plugin Popularity Contest in order to get it to print out a post category next to the post title. The current code is:

$posts = $wpdb->get_results("
			SELECT ID, post_title, comment_count
			FROM $wpdb->posts
			LEFT JOIN $wpdb->ak_popularity pop
			ON $wpdb->posts.ID = pop.post_id
			$join
			WHERE post_status = 'publish'
			AND post_date < NOW()
			$where
			$groupby
			ORDER BY pop.total DESC
			LIMIT ".intval($limit)
		);
		if ($posts) {
			foreach ($posts as $post) {
    			print(
    				'<li class="' . $oddli . '"><h4><a href="'.get_permalink($post->ID).'">'
    				.$post->post_title.'</a></h4><p class="meta">Topics:' . [CATEGORY GOES HERE] .  ' / <a href="' .get_permalink($post->ID) . '">'. $post->comment_count . ' comments</a></p></li>'
    			);

				 /* Changes every other <li> to a different class */
				if ('alt' == $oddli) $oddli = '';
				else $oddli = 'alt';

			}
		}

I need to somehow LEFT JOIN the terms, term_taxonomy, etc. tables and then put the category into the code. Problem: I have no idea how to do this.