Hi Beth,
I don’t have any specific examples to hand, I’m afraid, and as this is customization territory it’s really something we’d need to leave in your hands (bearing in mind you will need to be responsible for the code’s future maintenance) 🙂
The Codex itself is probably the best source of information on using post__not_in but essentially you would use it to provide an array of post IDs for exclusion:
$args = array(
/* ... other args ... */
'post__not_in' => array( 10, 20, 30 ),
/* ...more args ...*/
);
Of course you’d probably want to create the array of IDs dynamically and would create a separate query for that.