By being a chicken nerd and spending too much time in the coop! When you go to check for eggs and someone is on the nest, wait and watch until they lay. Then you can examine the shape of the egg or other "quirks" in their eggs that you can identify.
For example:
My light brahma lays an egg with a very pointy top
My EE is my only green layer, so that's easy
My buttercup is my only white layer, so that's easy
My BR lays a very large, more oval egg
My RIR lays an egg with tiny white speckles
1 welsummer lays a slightly lighter egg with speckles, the other lays darker eggs sometimes speckled sometimes not.