How do I power a ATmega328 with a coin cell battery
You use coincells the same way you use any battery to power an AVR like the ATMega328p. You hook it up directly. That's it, nothing different. Positive to VCC &amp; AVCC, Negative to VSS and AVSS.

Keep in mind, coincells have very little capacity, will drain quickly under 20+ milliamp load, so maximize the time you spend in power-save/sleep mode, and the low voltage will limit your clock speed to 4 or 8 or 10mhz at most.