What food would make my chickens lay speckled eggs? Can I get psychedelic colors by maybe feeding them broccoli and red beats? Can I encourage the chickens to produce these eggs if I surround them with pictures of easter eggs; you know, after I have colored them myself? My point is that the above answer of "By the food they eat" is short, curt, and sounding as if the question asked was too silly to deem worthy of your consideration. And as your screen name (Debossman) suggest, you must be a smug type with a bit of Napoleon syndrome.
By the food they eat.
It's not influenced by the food they eat. Hens that hatch out of speckled eggs may lay eggs with spots. It doesn't make any difference to the taste or nutrition, but most farmers don't breed speckle-egg layers because people are less likely to buy the eggs. Hope it was helpful?