Origin Industries' standard starship kitchen is a relatively nice one. It can be run in three ways: Like a fast food shop, Mess-hall buffet style, and like an actual restaurant. How it is run however, is up to the staff. It includes everything needed to cook: Ovens, grills, barbecues, stoves, microwaves, and almost any implement a chef could ever need. The menus depend on what food is stored on the ship.
Dishes are cleaned via a large dishwasher, which has the capacity to clean about half the dishes and utensils used by the kitchen. Cooking implements are hand cleaned in a large sink that is next to the dishwasher. This sink has a disposal system which grinds food into small particles that are eventually filtered out and recycled in some way.
Trash is disposed mostly with a trash compactor. The compactor has a 1M^3 capacity, and can crush things down to 1m x 1m x 5cm. These crushed pallets may be recycled or simply disposed of in port.