Just go to comment thread on the page it was posted (not in the notifications tab that drops down from the bell-icon).
Hover over your original comment, and a little "x" symbol should appear beside the 'edit' button on the top-right of the content box, with a tooltip popping up on hover saying "delete".
Click it, and you'll find that's exactly what it does... Deletes your comment!
To delete a post however, you'll need to click the little arrow in the top-right of the post, and select the "delete post" option from the little menu.