The instructions below are based on my experiences whilst upgrading my ESP8266 module to firmware version 0.9.2.2
Connect your ESP8266 module as follows:
You also need to download the new firmware and update tool from ElectroDragon: http://goo.gl/uHM6aO The firmware tool is called XTCOM UTIL.zip
Before you start the update, make sure your ESP8266 is working normally. Connect as above but leave GPIO0 floating and access the serial interface with a terminal program such as PuTTY. Set the baud rate to either 57600 or 115200 for later models. When you power-up the ESP8266 you should see some readable text indicating that it's ready. If you get nonsense try change the baud rate. If all is well you should be able to issue AT commands and get responses. Try AT+RST which should re-start the module. AT+GMR should give the firmware version. If all is well you can move on to the firmware update.
Her are the steps required to update the firmware:
On completion of the update, disconnect GPIO0 from ground and re-cycle the power. You can now use the serial connection to try a few AT commands. NB: Following the update the default serial baud rate changes to 9600 and AT commands require a CR/LF combination to enter commands.