Thumbnail images on category pages. Easy or no?

add <?php the_post_thumbnail(); ?> into the loop in category.php;

http://codex.wordpress.org/Function_Reference/the_post_thumbnail

(or in archive.php if there is no category.php; or make a category.php from a copy of archive.php and add the code there)

general to check:
http://codex.wordpress.org/Post_Thumbnails

http://codex.wordpress.org/The_Loop

the exact configuration will depend on the used theme.

please post any information about your current theme or a link to your site, or keep working with general links to the respective codex chapters.