If they are wood cabinets that are stained and have either polyurethan or lacquer, then this is the process to paint them.

First sand then to dull the finish, follow with a wipe down of mineral spirits (paint thinner), and then wash with ammonia and water (strong solution). These steps are very important as dirt and grease are your enemy to paint adhesion. Then you need to prime with a pigmented shellac primer such as BIN from Zinnser. The finish paint will be either an oil based or 100% acrylic enamel. I would go with an acrylic such as Sherwin Williams Pro Classic Acrylic Enamel which is made for cabinets as just any acrylic enamel will not work as they are not designed for cabinet work, because they don't dry hard enough. You also will need to apply two coats of the finish paint to get coverage and durability, and buy proffesion brushes to get a good finish.

Hope this helps out.