Though many would argue (including this author) that the source of our rights comes from our Creator, everyone would agree that the modern legalistic basis for our rights as Americans is the U.S. Constitution.
That document contains several Amendments, known as the Bill of Rights, which strictly forbid the exercise of certain types of power by the Government. There are only three Amendments usually implicated in a DUI case. These are the Fourth, Fifth, and Sixth Amendments (as applied to the governments of the several states via the Fourteenth Amendment).
If you look at the chronological progression of a DUI incident, it roughly follows the order of these Amendments. To illustrate: You are in a bar and you are drinking. You make the unwise decision to drive yourself home instead of calling a cab. Fourth Amendment concerns arise as the police stop you by the side of the road, and then decide if they are going to arrest you. Fifth Amendment concerns arise as they attempt to question and charge you. Sixth Amendment concerns arise after you are taken into custody and you want to speak with a lawyer.