The Esplora was not really designed for battery power. In the last two weeks I have used an Energizer "cell phone" backup battery into the USB port.
The more elegant (hack) solution is using a rechargeable LiPo battery. But this will not put out the 5 volts the Esplora needs. This is where an Adafruit Mintyboost works well to boost the 3.6 volts from the battery circuit boosts to 5 volts.
To feed the voltage in, I put it into the Tinkerkit output pins rather than the USB to create a lower profile and free the port for programming. Be careful not to have both connected at the same time.
Full details on how this was done are at http://21stdigitalhome.blogspot.com/2013/01/lipo-powered-arduino-esplora-game.html (http://21stdigitalhome.blogspot.com/2013/01/lipo-powered-arduino-esplora-game.html).
The project also adds an XBee radio that communicates via the two Tinkerkit digital pins which map to Arduino IDE digital pins 3 and 11. The only two free pins to hack around with if you use a display. I've documented the display interface if you want to hack those pins, see http://21stdigitalhome.blogspot.com/ under December.
cross-post with - http://arduino.cc/forum/index.php/topic,143371.msg1076748.html#msg1076748 -
Please remove one of the threads. (advice keep the other with the pictures, they look good!)