Go to a local meeting and they will go through a power point slide show of storms and tornados and stuff. They give you a card that has a phone number on it that you can call directly to NOAA's office.
This varies from office to office within the NWS. I know that some NWS offices issue cards after you "pass" a simple test at the end of their spotter talks, but the Indianapolis NWS does not.
To the OP, Tullahoma, Tennessee, is covered by the NWS office in Nashville. The list of spotter talks being conducted by that office can be found here:
Spotter Classes
Introduce yourself to the NWS staffer giving the presentation or to an amateur radio club member there to find out how to get involved with Skywarn in your area.