Firstly, make sure that you are connecting the module with respect to the guidelines stipulated in the datasheet. One of the most common errors is where traces run underneath the module, which generate noise. Also, make sure that both Vcc and Vbackup pins are connected, otherwise the module will not function.
If the module is implemented correctly, then you can proceed to test the communication. The quickest way to do this is by using using the test command: $PMTK000*32.
The test command should return PMTK001,0,3 (ACK OK). After testing the communications, wire it up on a PCB. Ensure that the antenna is correctly tuned and it corresponds to the reference.