How to read ASCII values from AT24C32 IC using Arduino? And what is serial.begin(?) in that EEPROM?
You have to know what the I2C address of your EEPROM is. Right now you have

#define EEPROM_ADDRESS 0x000


The example from the library you cite has this:

/**************************************************************************//**
 * \def EEPROM_ADDRESS
 * \brief Address of EEPROM memory on TWI bus.
 ******************************************************************************/
#define EEPROM_ADDRESS 0x50


Then, you have to create an instance of the Eeprom24C32_64 object:

static Eeprom24C32_64 eeprom(EEPROM_ADDRESS);


That sets up the object for the EEPROM on the right I2C address, so you can later use the eeprom object to read and write.