Read/Write external EEPROM

Hello!
I’m looking to read/Write some data from/to an external eeprom from my dmm. My multimeter is UniT UT139C . I need to backup the data stored and then to do some changes there.

I found this page related to my multimeter:
http://www.kerrywong.com/2016/03/19/hacking-dtm0660l-based-multimeters/

I don’t know anything about external EEPROMs. Can you teach me how to wire the arduino to my DMM? How is that sketch working regarding writting the data to the EEPROM?

The multimeter have the following pins for the external EEPROM(DM24C02A):
VDD
WP
SLC
SDA
V-

There is a good example over at Hobbytronics

http://www.hobbytronics.co.uk/eeprom-page-write

writing a page of bytes usually takes the same time as 1-2 single bytes.