Each Diet technology applies to one unit type and reduces the upkeep cost for that unit type by 10%. They apply to all units of that type trained in that city and are stackable up to 30%. The only units that do not have a Diet are Ox Wagons.
They can be researched at the structure that the unit type is trained at. Each level 15 structure can only research one Diet and each Diet has only one level. In order to reach the maximum of 30% a city needs 3 such structures.
Piky Diet applies to Hoplites (legacy naming convention, Hoplites were called Pikemen in an earlier version of the game). The other Diets are clearly named for the unit they apply to.