What is the most effective way to clean kitchen cabinets?

Try hot water, baking soda and Dawn.

I tend to use a soapy water Dawn solution for mild weekly cleaning and Murphy’s oil soap for more moderete cleaning jobs. Murphy's oil soap is an excellent all purpose wood cleaner.

http://homeguides.sfgate.com/clean-kitchen-cabinets-using-murphy-soap-104703.html

http://www.murphyoilsoap.com/home-care/murphy-oil-soap-uses ;

Hello! Best method to clean grime from hardware is a mix of vinegar, hot water, and Dawn detergent. Spray on hardware and let soak through the grime for several minutes. Baking soda should be used only if an abrasive substance is needed to scour. Otherwise scrub off grime and repeat if necessary. Good luck!

https://www.thespruce.com/how-to-refurbish-hardware-2878995

For the cabinets use Cabinet Magic available at Home Depot in the cleaning aisle....cleaner and polisher

Some people prefer Murphy's soap for furniture, I like Old English furniture polish. Either will clean your regular cabinets. I do it twice a year for maintenance. If they are super grungy due to years of neglect and super dirty, use this spray cleaner I will post. Put some in a small area and let it set for ten minutes or so. Scrub it off with an old toothbrush and reapply if needed. Here is the scrub for yrs of caked on dirt and grease:

To clean wood cabinets with Murphy's oil soap, you can follow these steps:

1. Dilute the Murphy's oil soap with water according to the instructions on the bottle.
2. Dip a soft cloth or sponge into the solution and wring out the excess liquid.
3. Gently wipe the wood cabinets with the damp cloth, making sure not to oversaturate the wood.
4. Wipe the cabinets again with a clean, damp cloth to remove any soap residue.
5. Dry the cabinets thoroughly with a clean, dry cloth.