You need to study:
- i2c protocol itself, this applies to all chips that is i2c compatible, not just pcf8574
- pcf8574 and hd44870 datasheets
You will be talking with pcf8574 using i2c instructing it to change its outputs as needed by the hd44870 display driver
Arduino has LiquidCrystal_I2C library, look into it, this is not an easy task if you want to implement all from scratch.