How to switch on and off an HD44780 LCD Display?
Assuming that display is initialized in 8-bit mode: to send command such as "Turn display on/off", 


set RS to LOW first (meaning it is command, not data)
set command bits on DB7-DB0 (in your case it could be 0x08 - DB2/DB1/DB0 all LOW to turn off following: display, cursor and blinking)
make a pulse on EN pin LOW-HIGH-LOW (take a 40uS delay before further communication)