The SIM800L must be powered with a voltage range of 3.4V to 4.4V. This just means that the Arduino will not be able to power this. do not connect to Arduino 5V pin because it will not work.
This module consumes a lot of power. During operation it can consume up to 2A of current and the arduino uno can not provide this much current.
The data pins of this module cannot be connected directly to Arduino because it operates on 3.3V and not 5V
If the LED indicator blinks every second, it means the module is searching for network and has not connect to any network yet. if the LED indicator blinks every 3 seconds, it means the module has connected to the network and this is our goal
Solution
Use lithium-Ion battery (3.7) or use LM2596S bulk converter. Either of this will give accurate voltage and enough current to the SIM800l.
To interface the SIM800L data pins with Arduino, use a voltage divider. connect a 10k ohms resistor from the RX pin of SIM800L to Arduino pin and connect a 20k ohm resistor from that same Arduino pin to ground.
Ensure that the wires use to power this GSM module are very short and thick.