What cleaning solution should I make/buy for use on my cupboards?

Krud cutter brand is great! Get the spray particularly for kitchen cabinets. You can get it at Home Depot, Lowes.

What is on them? What are they made from?

For example my cooking oil bottle had a drip down the side that made an oil ring on my shelf and I have melamine-faced shelves. That took two applications of degreasing detergent (like Dawn) on a nylon scrubbie sponge.

They are wood and it is just grease build up on them

daily cleaning: OrangeGlo

slight build up: a past of baking soda & peroxide, scrub with a toothbrush

serious build up: GP66 or Fuller or another kitchen safe degreaser

thanks for the info