To start with: your code is correct. I copied-pasted it to my own Arduino IDE and uploaded it to an Arduino Nano connected to a LCD. The LCD displays: Hello, World! and on the next line appears a rapidly increasing counter.
So far so good. If 'nothing'; happens, please check all the wires between your Arduino and the LCD. You can enjoy a wiring scheme on my website:
If then still nothing happens turn the potentiometer to change/improve contrast (background illumination should be visible all the time)
If then still nothing happens: return to this forum and show clear pictures of the wiring and of the LCD.