To delete a reply (that you've posted), click on the Edit button at the bottom right of the reply. When the edit window opens, click the Delete button and confirm (in the dialogue that follows) that you really do want to delete it.
For a thread (that you've started), you can edit most of the content out of the first post but you can't get rid of the whole thread yourself, especially if other members have replied. Click on the Report button (

) to the left of the first post in the thread and let us know that you'd like the thread removed.
You can also use the report button for posts (or threads) that are older than four hours so you can no longer edit them yourself.