How to clean kitchen cabinets?

Ok serious answer. If in fact they are urethane, start with Dawn. If that isn't quite strong enough, step up to Barkeeper's Friend powdered cleaner. It will clean and polish most anything and not scratch the urethane finish.

You will never go wrong with decent Degreaser.. by decent i mean the one you buy at the autobody shop that sells car paints, thinners, and all that jazz. By decent i mean high concentrate used to pre clean surfaces before painting on car body parts. Spray that stuff (small quantities even) and it dissolves everything that is biological and did not get shipped with the new product. It is safest way of removing tough grime (even 10 year old engine oil!). I would advise wearing gloves and goggles as i had some in my eye by mistake.. ouch!

You said 'urethane' - I guess that's gloss finish? If its wood.. it more complicated as you dont want to dampen it. So just small steps and lots of air to dry it.

First is to wipe off all the dust and debris in the kitchen cabinet. For the stubborn grease and grime, try a degreaser- Goo Gone All Purpose Cleaner is a good one. (make sure to wear gloves because they can cause an allergic reaction if you have sensitive skin) OR you can also DIY with a damp cloth and undiluted vinegar. Wipe the greasy surface until all the grease comes off. Let the kitchen cabinets dry completely by keeping the doors open.

Hey below is the general home DIY recommendation for cleaning kitchen cabinets without loosing its shiny and glossy effect, this is what even I do at my place.

1. Consolidate a spurt of Dawn dish cleaner/soap into a bucket of hot water, technically add half teaspoon / 8 cups of water, you can use dipped into solution scotch brite heavy duty scrub sponge for washing the cupboards I too prefer this, you can also use used tooth brush for area with access oil or grease.
2. After applying the first step you'll notice cabinets are bit soapy, so just wipe them down with clothes plunged in simply heated water.
3. Last step fill a bucket with 1 gallon of water and 1/4 cup of Murphy Oil Soap(as per the direction given in bottle) and do another wipe to make the cupboards sparkle and get rid the unwanted smells. And here you'll end up with and incredible cabinet look, all perfect with rich woods tones radiating through! Do let me know if in case of any query.