This is a simple improvisation of the "Experiment 48: 2-bit LCD" from Myke Predko's 123 PIC Microcontroller Experiments for the Evil Genius. Instead of a PIC microcontroller, Arduino is used in this experiment.
Connect the Clock to pin 3 and the Data to pin 2 of the Arduino.
You can refer to the old webpage and the schematic there.
The code from pages 127, 128 and 227 are slightly modified to have these run good at Arduino platform.