The shade of blue varies from hen to hen, so you make sure the rooster you are using is also out of a blue egg. You pick the bluest eggs the hen lays to hatch. Then with the hatched pullets you pick the darkest blue eggs, each succeeding generation is theoretically capable of producing bluer eggs. I am not sure just how blue you will be capable of acheiving, but, I have seen some nicely colored blue eggs.
If you cross a rooster from a blue egg on a white egg layer, you will get a pullet that lays blue eggs.
For green eggs, you cross a rooster from a blue egg with the brown egg layer. The resulting pullets will lay a green egg, the shade of green is determined by the shade of brown from the hen.
I don't know exactly how it works if you cross a rooster from a green egg with a hen that lays green eggs.
I suspect you will get some green egg layers and some brown egg layers. Because green egg layers have blue and brown genes combined to lay green eggs.