I had also trouble with it, and I also used the library by Rob Tillaart.
First of all, the 24C?? EEPROMs are not all the same. Which one do you have ?
You can start by reading and writing a byte to a certain location in the EEPROM.
Next thing is the 'page'. The EEPROM has pages inside, and you can't write beyond the page.
To be able to write any length of data to any location, you need to split the writing according to the pages. That is why that library contains all that code.
If you can read and write a single byte with your own sketch, you can use the library, even if you don't understand all of it.