This project requires just a few components: (Arduino) Uno Mk3, 'worlds smallest' SIM800L module (fitted with a male header and plugged into a breadboard), 3 x LM2596 2A step down power converters, a suitable level shifter and a 12 volt power supply. I have also used a decent aerial for the SIM800L module rather than the piece of bent wire supplied. I am in the UK and I am using an Asda Mobile prepay SIM card (EE network).
Adjust one power converter to output 4 volts. This is for the SIM800L module. Adjust the second to 5 volts for the Arduino and the third one to 2.8 volts for the level shifter (necessary because we don't have access to VDDEXT with this SIM800 module). The voltages differ slightly from those in the photo as I trust my meter more than I trust the power converter displays! Connect the level shifter to the module and the Arduino, Rx -> Tx, Tx -> Rx. Don't forget the grounds!
Now load a simple Serial Relay program to confirm that the SIM800L is alive and talking.