Arduino and ESP8266 Two-way Communication
See How can I verify that my ESP8266 is working? asked 2 hours before.

use something like https://www.sparkfun.com/products/12009 or https://learn.adafruit.com/arduino-tips-tricks-and-techniques/3-3v-conversion

Usual way is let the Arduino direct the ESP, but if you are able to program ESP too, then any communication can work the same way as between twou ESPs or two Arduinos (with the level shift in mind)