As I previously told I couldn't find anything suitable with google. There are some sites which talkin about this topic but in general, they are rather complicated to understand.
The thing which I want to emulate is known as: RGB Matrix – Serial Backpack
According to Eagle schematics they're using 3x 74LS595D, 1x AVR Mega8 and 1x ULN2803. My goal is to achieve this to work on breadboard. It isn't easy but it is OK