1) If you are the person who began the thread, you should see a list of Actions on the right hand side of the screen that includes the option of Delete:
2) If you have made a Reply to an existing thread, you should see an Actions dropdown in the lower-left corner of your reply, and Delete should be one of the options in the dropdown:
Note that my screenshots were taken as an administrator, with admin privileges. However, I tested them a moment ago using an account with standard access.
I also believe it only lets you edit/delete the post for 5-10 mins. But I could be off on the time frame.
Perhaps it's not a timeframe -- but once someone replies to it, you can no longer delete it since it has become a dependency.