Comments are posted on specific items, like site member profiles, individuals in the family tree, photos, etc..
In order to delete a comment, go to that page (for example, if the comment is on a photo, go to the photo page).
At the bottom of the page you will see the set of posted comments.
To the right of each comment there will be a small x icon. Click that icon in order to delete that comment. Note that you need to be logged in as the site manager in order to be able to delete comments.