EEPROM - 24c08, need some guidance

Assuming you have a 5V part (I haven't checked the data sheet)
You wire the SDA and SCL to the I2C pins on analogue 4 & 5 and wire 4k7 pull up resistors on each pin.
There is no address pin on your device so it will use a fixed I2C address.
The mode, PRE can be wires to arduino output pins id you want to change the mode of operation otherwise you can just hard wire them to Vcc or ground. The E can be wired to an arduino output pin so you can enable it in software.