Communicating with a bluetooth module

It currently isn't talking to anything. I can pair my phone and computer with it but that's it.

Then, the bluetooth device IS talking to either your phone or your computer. It's just that nothing gets from the bluetooth device to the Arduino, because you haven't written that code.

"That code" consists entirely of Serial.write(), Serial.print(), Serial.println(), Serial.available() and Serial.read() statements in the proper order, with the proper things being sent.

Normally, knowing what to send is easy, because the bluetooth device provider tells you exactly what to send to the device to make it do something, and tells you exactly what the return data means.

Where you saved money was on the documentation. It appears that you got exactly what you paid for.