Blank output in serial monitor
Step 1) Check RX TX connections
Step 2) Change your baud rate to 115200. Turn off your arduino. Turn off gsm. Start your gsm first and then your arduino.

or 
Step 3) Upload Software Serial code and just send "AT" without quotes using serial monitor. If your connections are correct you should get reply as AT.
Also make sure to set the baud rates to 115200.
Most of the GSM modules have default baud rate at 115200 or have auto baud adjustment enabled but need to be power cycled.