How can a begin preparing a good case to contest a DWI? Does taking a drug screen help? Should I be contacting witnesses I was with the 7 hrs prior?

If you have experience with legal processes in criminal court then establish a time line and line up your witnesses, get all discovery from the state and prepare the defense. There is nothing simple about a trial and the technical skill necessary to present evidence requires some knowledge of the system. If you lose the case you will have a conviction for your lifetime, surcharges in the thousands of dollars, fines, court costs and jail time or probation.