How do you get a really smooth finish when painting cabinets?

Use very little paint on your brush. After you dip just the edge in the paint, wipe it across news paper or similar to minimize the paint. Better to apply more coats tan a thick coat. Buy the best brushes you can afford.

It might depend on the type of brush you're using -- if you have one that's smooth bristled and not coarse, that helps. Or you could try a paint sprayer.

the is a product normally used with spray painters, it changes the viscosity of the paint making it easier to spray With no splatter marks. Try adding small amounts to your paint, until the brush marks disappear.

Try using a small foam roller and one of those foam paint applicators for the smaller areas and corners.

Go to a good paint store, not a big box store. Ask their advice on paint that will flow the best, don't skimp on cost. There is also an additive called Floetrol that replaces some of the "good stuff" that the government made paint manufacturers take out of their paint that used to make painting with a brush so much easier. The can tells how much to use. As others have said, use a good brush, maybe not the most expensive one but for sure not the cheapest and clean it well after each use.

Use the best quality paint and brush you can afford.

I think there is special paint for cabinets that won't show brush marks.

https://www.cravingsomecreativity.com/paint-without-brush-marks-strokes/