I am trying to display just post title and their links within a set category. However I am running into issues understanding the Codex. Any help or guidance would be greatly appreciated.
It seems that you are working on your templates. It basically means that you need to edit correct template and insert the right tags.
Firstly, you need to understand how the template is chosen. WP has special hierarchy for every view. Home page is usually home.php and categories are category.php or category-1.php. If any file is missing, WP simply takes next on the list. Last on the hierarchy list is index.php which is chosen if no other file is found. [http://codex.wordpress.org/Template%5FHierarchy#Category%5Fdisplay%5D%5B1%5D
Secondly, look at the template tags. Displaying only title with link means you need title and permalink tag. Anything else is optional.
I use this a lot in my blogs. Helpful when you want to display featured items or such.
http://codex.wordpress.org/Template%5FTags/query%5Fposts#Category%5FParameters
http://codex.wordpress.org/The%5FLoop#Style%5FPosts%5FFrom%5FSome%5FCategory%5FDifferently
You might have seen the above link. I'll explain how it works.
Posts are loaded using the loop. If you do a Query Posts just before the loop, you can choose from select category (or many categories) and also limit the number.
<?php query_posts('cat=1&showposts=5'); ?>
<?php if (have_posts()) : while (have_posts()) : the_post(); ?>
<li><a href="<?php the_permalink() ?>"><?php the_title(); ?></a>
<?php the_excerpt() ?>
</li>
<?php endwhile; endif; ?>
You can use the above code as many times you wish. Choose the category ID (can be found from the admin) and the number of posts you wish to show.
Comment - if you require additional help.