A document created in Google Docs can be deleted using the options available as part of Actions menu. You can delete a document by selecting it from the document list and right clicking on the selection or by clicking down arrow available as part of Action menu.
From the menu list select Move to bin option then click the Bin for everyone button in Deleting shared items pop up (if displayed)
Now navigate to the bin directory and select the document which needs to permanently deleted.
On right clicking the selection a context menu would be displayed as shown below. Selecting Delete forever option would delete this document permanently.