You can find our Nokia Display Arduino library on github. You should install it through the Arduino Library Manager.

Open up the Arduino Library Manager:

Search for the Adafruit PCD8544 library and install it

Search for the Adafruit GFX library and install it

If using an earlier version of the Arduino IDE (prior to 1.8.10), also locate and install Adafruit_BusIO (newer versions will install this dependency automatically).

We also have a great tutorial on Arduino library installation at:
http://learn.adafruit.com/adafruit-all-about-arduino-libraries-install-use

You should see the pcdtest example in File>Examples>Adafruit PCD8544 Nokia 5110 LCD library. Load that example and flash it to your Arduino

You can control the backlight, its much brighter when you connect the backlight pin to 5V (you don't need a level shifter if you are using a Nokia display from Adafruit). You can control the backlight using an Arduino pin since there is a transistor on the board.