Inserting thumbnails on the home page

find the template for the home page –
could be index.php (or home.php – see http://codex.wordpress.org/Template_Hierarchy) depending on your theme.

try to locate the loop http://codex.wordpress.org/The_Loop

try to find te line with the_excerpt() or the_content()

then possibly add the code for a thumbnail before that line
http://codex.wordpress.org/Function_Reference/the_post_thumbnail

details of formatting might depend on your theme.