thumbails and tags

Hi there, i’m new using wordpress and i only use it because a costumer want to readapt a theme he is already using.

I have to edit the size of the thumbs for each post, but i dont understand how the system select the right thumb for each post and tag?

I explain the problem.
The site is a news paper online, with the tags he select where it goes the new to publish, so i edit the theme and make that select the X number of items that will show for that tag.

But the problem is to set the right thumb, and how to make all the thumbs.
aparently the theme have some functions that create the thumbs:

function XXXXXX_setup() {
add_theme_support( ‘post-thumbnails’ );
add_image_size( ‘mainimage’, 350, 230, true );
add_image_size( ‘home-thumb’, 80, 60, true );
add_image_size( ‘home-slider’, 150, 115, true );
add_image_size( ‘cat-thumb’, 120, 88, true );
add_theme_support( ‘automatic-feed-links’ );
register_nav_menus( array(
‘topmenu’ => __( ‘Main Navigation’, ‘XXXXXXXX’ ),
));
}

but i just dont understand how make the system to select from this list the right image to show when i call the_post_thumbnail()

could some one explain or give me the links to understand more about this please.