Using the Stereo audio output would be the simplest way... you'd need to write your own app.
or you could use BT, USB, wifi, NFC, or IR (depending on the phone).
Arduino already make boards that can communicate with phones through BT or USB or Wifi. and there are already apps to available.
It all depends on where the phone is relative to the circuit. If the phone is close to the circuit then BT, WiFi or USB. If you carry the phone with you while the circuit is at home, then either SMS messages (may be not free) or through Internet.