SIM800L is nice and inexpensive GSM breakout board. We will set it up with Arduino and send simple text messages. The library can ofcourse be used to do more things like calls etc., We will focus on setting the module the right way because you'll have to take care of a few things like power and reset.
Hookup
We will hook up the SIM800l module with Arduino using the Soft Serial library. We will connect the Hardware serial port to the computer to debug and print messages.
Reset Circuit
Power
Note that the module requires voltage in the range of 3.17 to 4.4v . If proper voltage is not provided the module will give under and over voltage warnings. Hence we used a 3.7v LiPo battery. You may also use a regulator like LM317.