These modules, as per the datasheet ("SZ05 product manual"), have a peak current of 250mA. For the Mega, it seems the regulator is rated for a maximum current of 800mA.
I'm currently in the process of integrating these modules for a projet and they work fine.
What I did is connect GND, VCC (5V), RS1 (TTL receive), TX1 (TTL send), CFG (to 3.3V), SLP (to 3.3V) and the LEDS to RNU, NET and ALM. I had to leave the RET (Reset) pin unconnected (even though the doc says it is low effective)
To configure it :
First, open any terminal on the serial port on which the evaluation board is connected (configuration is always 38400 bauds)
To enter the configuration mode, press the button (on the evaluation board) or tie the CFG to ground for 3 seconds.
The module then asks which language to use, select English by entering "2".
Next, type "SHUNCOM". You should now see a menu to configure its settings.