Expect the plumber to ask which fixtures are slow, when it started, and when the septic tank was last serviced. For a single fixture, the fix is usually at the trap or a short branch line. For a main-line backup, the plumber will look for a cleanout in the basement and run a cable or water jet toward the tank.
If the line clears and then backs up again, a camera inspection can show roots, a sag, or a broken section and how far from the foundation it sits. If the camera shows an open pipe but water still won't drain, the trouble is likely in the tank or leach field, and the plumber should tell you so plainly.
Routine clearing doesn't usually need a permit, but replacing drain piping can. In Hanover, plumbing permits come from Building and Inspectional Services through the Town's OpenGov portal.