How to show only headlines on the front page

create a home.php template, and just drop the tags for content or excerpt within the loop.

can I just backup and edit my existing home.php file or is there a special template somewhere?

If you already have a home.php, then yes, your post is correct. Backup, remove either the_content or the_excerpt

OK thx miklb. How do I go about creating a new template for other post pages I want to create?

Like use the current home.php page but take out the side bar or rework the design for specific post pages.

Can this be done at wordpress.com also or is it not possible to make such changes? Or is there an alternative?

No and wordpress.com has it’s own forums