To make modifications to the theme, you are only supposed to modify your theme files.
In order to edit files, you can use any text editor such as Notepad, or if you want, a code editor such as Dreamweaver (paying), or any other code editor.
As for what you are asking to do, are you 100% positive you want to do that? Because if you do, then your readers will not be able to access your posts individually for reading, commenting, etc. If you understand these implications, then do follow the following steps to remove links to posts in the home page:
1. open your
index.php with the text/code editor of your choice;
2. Locate line 12 of that file, which reads:
<h2 class="title"><a href="<?php the_permalink() ?>" rel="bookmark" title="<?php the_title(); ?>"><?php the_title(); ?></a></h2>
3. Replace that line with this one:
<h2 class="title"><?php the_title(); ?></h2>
Presto, you are done!