Just below your question you should see several links: share edit close delete flag. Click on the one which says delete. (If you hover over this link, the tooltip says: "vote to delete this post". I agree that this might sound a bit confusing.) The same is true for answers.
When you click on delete, a pop up window will appear. It will either ask you to confirm whether you really want to delete your post or explain the reasons why you cannot delete the question.
In some situations you are not allowed to delete your own question. For example, you cannot delete a question which has an upvoted answer (or an accepted answer or more than one answer).
For answer-deletion there are less restrictions. Yet an accepted answer cannot be deleted.
And unregistered users are not allowed to deleted their posts at all.
More details about deletion can be found here: How does deleting work? What can cause a post to be deleted, and what does that actually mean? What are the criteria for deletion?