To make this you should have some coding knowledge. It depends on your theme, if you have category.php then change the loop in this file, if you don't have this file, then change the loop in archive.php.

Knowing what theme is active on your blog would make things easier.

To add to what the reply above said: if you don't have a category.php in your theme (very few themes have, btw) then just save your archive.php as category.php.
Warning, look for the "singular" i.e. archive.php because the "plural" archives.php is something different!

After that find in it the line that says:
<?php the_content(); ?>
Delete it!

Done.

No. When you click on a category name it is NOT the custom Archive PAGE that is displaying your posts. It is one of the so-called multipost templates.

In "normal" WP (which excludes most of the frameworks that are made solely to confuse the users...) basically there are 3 kind of templates:
- multi-post templates - e.g. index, archive, category... templates that will display more than one post
- single post template (single.php)
- Page templates

They have different roles and different capabilities.
You want/need the multi-post type of template for your categories.

WP works in this way (without telling you the technical details):
when you click on a category's name (link) WP starts looking for these template and in the exacvt order as outlined below =

- category-XX.php (where XX is the cat ID and will be used to display posts ONLY from that cat); if not found then
- category.php - for all cats; if not found then
- archive.php (also used to display monthly, daily...time-related archives)
- index.php or main template - the general fallback file for any missing template

Now, the problem with paid themes/frameworks is that unless you find somebody that is
a) also a user of the theme/framework
b) know WP and doesn't talk nonsense...

it will be very difficult to get reliable advice.

Since you are a paying customer, and now you know exactly what you need... you can go back to the framework's support and ask them

Thanks for your explanations.
Unfortunately, their support don't seem willing to be helping me.
Here's what they say:

"Thank you for your question. Unfortunately, we are not able to provide assistance with this, as it will require customization to your theme’s code. We have a growing collection of code snippets that can be used as a starting point for many customizations. You can find the code snippets at Code Snippets - Genesis Framework

If you find that these code snippets are not sufficient or if you need additional assistance we would encourage you to post your question to our community forum where other users and developers can provide suggestions on how to proceed. The community forum can be found at StudioPress Community Forums

For more comprehensive theme customization solutions we have compiled a list of Genesis developers that may be able to assist for a fee. The approved Genesis developer list can be found at Genesis Developers

Thank you for choosing StudioPress."

I think they're not very fair... I paid for the theme and I'm only asking for some explanations on how to do something very simple.
Don't you agree ?

Sorry to hear that.

Of course, I should have warned you to ask your questions in a very simple way - since most support people are dumb

I don't know ho you phrased your question, but it should be something like this (to support or post in their forum):

"Which template file is used to display the category archives, i.e. to show the list of posts from a category when clicked on the category name? Please, I need the exact name of that template file!"

That's it, nothing else. When you get a precise answer, we can go from there...