Which pins does the Efcom 1.2 GPRS shield require to be connected in order to work?
The serial connection uses the pins D0 through D3.  RX and tX are selectable by jumper on the GPRS module.

In addition, you will need ground and power.  The GPRS module uses the Vin from the Arduino connector (on the same row of pins as reset, 3V3 and 5V) for power.  It also uses the 3V3 to power the LCD.

Finally, D5 can be used as a reset on the SIM9000, and D6 is a kind of enable input.  This must be set correctly to enable the SIM9000.

It appears that you also need to connect D4 as well.  It doesn't seem to be used by the software examples, but it is connected to the SIM9000.

Also, does the module work without the LCD when connected directly to the Arduino?

Given that, you should be able to puzzle out which pins of the Atmega chip are actually used for what.