I know nothing about this device, but it doesn't seem hard to identify the connections as a lot of signals are labelled on the other side at the unpopulated 12 pin connector at the bottom.
The 6-pin connector labelled COM1 will be communications, but without experimentation we don't know what it implements in terms of functions or protocol. You'll basically just need to connect something to it and see if anything comes out, and if so experiment with baud rates until it looks sensible. Often these devices just dump a reading once a second in plain text, but sometimes the data is binary or requires a query command in a certain format.
My guesses are as follow: (Edited to swap pin 1 & 2)
Pin 1 is receive data, and probably no too useful if you don't have software or documentation for the protocol
Pin 2 is transmit data, and probably what you are most interested in
Pin 3 is hard to tell, but I'm guessing GND due to the protection diodes - you can check continuity
Pin 4 is 3.3V (output from the device)
Pin 5 is unknown - maybe another GND connection to pair with pin 6
Pin 6 appears to be a 9V power input, but diode D5 isn't populated so it probably doesn't have any function
I would also guess that these are 3.3V level UART signals, so you will need a 3.3V USB to serial adapter, and initially just connect GND and pin 1 TX to the USB to serial RX pin. Pin 1 on this connector is the square solder pad on the left of photo C, so on the right of your photo B. Edit: this is actually the reverse pin order of a JST PHR-6.
The 4-pin connector labelled JTAG1 (and most of the 12-pin unpopulated connector) is probably something you should avoid unless you know what you are doing.