Start by plugging your Feather into the wall socket with the micro USB AC adapter. If you have an infrared thermometer this would be a good time to use it. Measure the temperature of your thermometer and make sure it is behaving like you expect. If you don't have an infrared thermometer try this:
Check for the OFF position - To increase the temperature hold the thermometer in your closed hand, it should exceed 27C (~80F) quickly and the power should turn off. When the power is off the red indicator light on the PowerSwitch Tail AND the LED light on the Feather should be OFF.
Check for the ON position - Place the thermometer, temperature sensor side down, on a cold surface (a hard counter or window should work, if not, try the fridge). Once the temp is below 24.5 C (~75F) the power should turn ON. When the power is ON both the indicator light on the PowerSwitch Tail AND the LED on the Feather should be ON.
If you're confident that your thermometer and thermostat code are functioning you can start connecting the pieces. The schematic below is an overview of my setup. Start by securing your thermometer to your kombucha brew vessel with electrical tape. Make sure the temperature sensor is touching the brew vessel. Next attach your heater to the kombucha vessel. Plug the PowerSwitch tail into the wall outlet and plug the heater into the PowerSwitch Tail. Next plug your Feather into a wall outlet with the micro USB AC adapter. Observe your thermostat over the next few days to ensure that everything is functioning normally. Last but not least, brew for 5-7 days, and ENJOY YOUR 'BUCH!