You can delete them after a short period, after that they do not delete. If you put it in the wrong place go to site feedback and ask them to move it. They usually will.
In the lower left corner you'll see the three options; "Edit," "Delete," and "Report." Select "Delete." When the "Delete Post by Jesse" comes up just click on "Delete Post". There's no need to give a reason. And Mindmaster is quite right. You don't have all day to do it. If you don't see the "Delete" option then the option has closed and you'll have to appeal to a mod to do it for you.