take a look at the AT24C64 datasheet. it shows the 2-wire interface protocol which is also called I²C. You can find lots of bitbang code for this on the web. there are also pull-up resistors needed on the data and clock lines. I believe microchip has an applications note on interfacing to an I²C device. It is a bit complex.
You may not want this advice but I'd look at using eeproms using SPI instead of I²C - it is much easier to "bit bang".