Example of how to drive a 1602a LCD from an AVR ATmega32u4 with a 74HC595 shift register.
Wiring
32u4 PD0 - 1602a E
32u4 PD1 - 1602a RS
ground - 1602a R/W
32u4 PE6 - 74HC595 DS
32u4 PB5 - 74HC595 SHCP
32u4 PB4 - 74HC595 STCP
pull up - 74HC595 !MR
ground - 74HC595 !OE
The 74HC595 should have Q0-Q7 wired to D0-D7 on the LCD board.
Example
