First you would need to reverse engineer the assembly language from the binary image on the EEPROM. Then you'd have to understand it
Not a simple task, but do-able. From that you could glean clues as to how the card actually works. Much of it will be a standard operation as most VGA cards at the most basic use the same style interface. For more complex work, like graphics, you'd need to know just how the card works - for that you may get some detail from things like the Linux drivers (which should be open source) for the card.