If the posts are already shown on your page, just with a bunch of unnecessary text that you want to take away, do the following:
1. Open the template file of your homepage (it can be named different in different themes, so impossible to give you the exact name of file, but usually they are named like index.php or home.php).
2. Look for the following bit of code:
<?php while (have_posts()): the_post; ?> // indicates beginning of post loop.
..... // there might be some other lines of code here, but eventually you will find a line that contains:
<?php the_title(); ?> // keep this line
..... // you can start deleting code that follows after the previous line one by one line and see what happens.
<?php endwhile; ?> // Do NOT delete this line, this indicates the post loop end.
When I experiment with code and feel unsure, I change one thing, save, refresh the page in browser and act according to the result. That way you can always press undo if stuff goes wrong. If you are completely new, I suggest you save a copy of the file you are editing so if everything goes wrong you can just replace the damaged copy with the original file and start over.
Suggested reading: http://codex.wordpress.org/The_Loop
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solved Show post titles only on the homepage