In Tennessee, citizens can register to vote in person or by mail. You must be both a U.S. citizen and a Tennessee resident and 18-years-old or older on the next election date. You must also be registered no later than 30 days before the election.
To register both in person or by mail, fill out the application form (SS-30100) which you can find HERE.
You can then mail the form (postmarked no more than 30 days before election) to your local county election commission.
You can also take it to your local clerk's office, library, deeds office, Department of Health, Department of Human Services, DMV, Department of Mental Health, or Department of Veterans affairs.
-NOTE: If you have recently moved or changed your name, the form should be filled out and sent to the local election commission office.