What is the best way to clean/shine kitchen cabinets?

http://homeguides.sfgate.com/put-shine-back-kitchen-cabinets-97897.html

I always use Old English furniture polish. It cleans and treats the wood too. It is best if the cabinets are not too grimy, otherwise use warm soapy water with just dishsoap or something mild first. Then do apply the Old English over that. You do not want to get the cabinets real wet if you do wash with soapy water first. Wring out the rag well, then rinse too. Old English comes in dark or light depending on the wood you have.

Old English is great, my mom used it and I do too. I use their lemon oil, too, for some things.

http://www.trendswoodfinishing.com/blog/how-to-properly-clean-your-wood-cabinets-so-they-shine.html

The simple cleaning process is first empty the cabinet and deep clean the cabinet with microfiber cleaning clothes only because this cloths remove dirt and grime from the cabinet surface completely and absorb itself.