Because cookware comes in many types of materials, there are several clean up considerations. Some of your cookware can be washed in the automatic dishwasher but most do best being washed in hot sudsy water using a nylon scrubber. Hard water tends to darken the aluminum finishes. Use a paste of water and cream of tarter to remove these dark spots. To avoid scratching the finish on the anodized aluminum, do not use an abrasive cleaner.
Wiping with a clean paper towel best cleans cast iron cookware.
You can run hot water over stuck on food but then it should be dried completely. If left wet, cast iron will rust. To prevent it from rusting, set the cookware piece on the stove over high heat until all moisture is evaporated and then coat with oil before storing.
Use a copper polish to keep copper cookware from tarnishing and to prevent white spots. There are stainless steel cleaners that can be used on the stainless steel cookware to remove stains and restore the shine.