If you are logged in to Facebook, it's easy to edit or delete a post.
Click the tiny arrow at top right of the post you want to edit.
Then select an action. If you do not see the action you want, it means the user you logged in with does not have the appropriate rights.
"Highlight" lets you star the stories that you think are important. Starred stories are highlighted on your Timeline and include a star banner.
"Turn Off Notifications" means you will not receive a notification whenever someone comments on that post.
"Hide from Timeline" will hide the post from your Timeline. It can be unhidden later if desired.
"Delete" is permanent and cannot be undone.