Remove them from the cabinet and remove all hardware. Label inside of door with a piece of blue tape to get them back in the proper place later. Clean the doors and lightly sand. Paint with a good quality latex enamel (washable) paint. You can also add a coat of water-based polyurethane for extra protection. You will probably have to do the same thing to the cabinet face frames. Reinstall doors. The hardware may need to be cleaned before installation.
It would be easiest and look the best if you take the cabinet door off the cabinets. How you prep the door fronts depends on what you want to paint them with and what the doors are made of.
Here is a great tutorial for painting cabinets https://www.remodelaholic.com/how-to-paint-cabinet-doors/