I would like to feature a tip on the homepage

You can place another loop on the template, for example below the first loop.
Multiple loops documentation: http://codex.wordpress.org/The_Loop#Multiple_Loops_Example_1

<?php if (have_posts()) : ?>
           <?php while (have_posts()) : the_post(); ?>    
           <!-- your first loop ... -->
           <?php endwhile; ?>
 <?php endif; ?>

<?php
wp_reset_query();

$tips_query = new WP_Query( 'category_name=tips&posts_per_page=1' );
?>

<?php if ($tips_query->have_posts()) : ?>
           <?php while ($tips_query->have_posts()) : $tips_query->the_post(); ?>    
           <!-- do stuff ... -->
           <?php endwhile; ?>
 <?php endif; ?>

<?php wp_reset_postdata(); ?>