What is the best way to clean dark kitchen cabinets?

Any degreaser should work, I wouldn't scrub to hard though. You didn't say if they are a dark paint or stain. If they are painted hard scrubbing will take the paint off.

If wood, Murphy's Oil Soap works well. Otherwise Dawn dish soap or a vinegar water solution.

Hi Lesia, Mix together 1 cup (240 ml) of white vinegar with 2 cups (480 ml) of warm water. wipe down greasy cabinets. Rinse your cloth with warm water, wring out most of the moisture, and use it to rinse the cabinetry. Dry the damp surfaces with a paper towel, but note any still-sticky spots that need a second attempt.

Microfiber clothes (like Norwex) and water work miracles!

I use TSP substitute mixed with water in a spray bottle and a rag. Cleans cabinets with practically no effort.