The FYTA Mini uses a CR2450 coin cell battery.
CR2450 batteries are available at supermarkets, pharmacies, and online. Battery life is typically up to 12 months. The app will notify you when it's time to replace it - the sensor will also flash red when you press the button.
To replace: turn the battery compartment cover to the left and open it, remove the old battery, insert the new CR2450 with the correct polarity, and close the cover by turning it back to the right. The connection to the app will restore automatically.