To make the ESP01 or other in that family work, you will need to reflash the FW (you cannot configure the standard FW to work as it doesn’t support a ‘pass through’ mode on the serial*
Download this image http://www.communistech.com/files/esp8266/firmware-1.0.0.bin You will need to set Telem2 serial port on the Pixhawk to 921600 i.e. SERIAL2_BAUD = 921
Updated: there is a newer version http://www.communistech.com/files/esp8266/firmware-1.0.11.bin available now.
You can do this by connecting using Mission Planner or APM Planner 2.0
MAV Pilot Settings are 192.168.4.1:14550 UDP