What should I do if I had a former employer tell a potential employer that he fired me for drinking and being drunk on the job which is entirely untrue?

You could sue your former employer for defamation.  Defamation is a false statement made with knowledge of its falsity communicated to a third party who recognizes the defamatory content and the statement is injurious to your reputation.  Each repetition of the defamatory statement is actionable in a lawsuit for defamation.

Libel is written defamation.  Slander is spoken defamation.  Your damages (the amount of compensation you are seeking in a lawsuit for defamation) can include mental distress, loss of friends and associates, and if applicable physical illness and medical bills.  These items are referred to as general damages.  Since the slanderous statement is one that is incompatible with your employment, you can recover general damages without proving pecuniary loss (lost income).  Pecuniary loss would be special damages.  You may want to include lost income in your damages if you are not hired for that particular job you mentioned because of the defamatory statement of your former employer.  You will need to file your lawsuit prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.