On Facebook, you can go to the top right corner of your post, or your own comments on another post. There is a small arrow which is a pull down menu. When you click on it, you will be given options to either edit or delete your post for that thread. If it other peoples post that you wish to delete, you can't. All you can do is either ignore that person or hide the post, but the comments will still be visible to others. You have no control over other peoples posts, only your own, and your personal preferences of what you choose to see.
Edited by SFNative (06/29/15 05:13 PM)