Place a stopper in the kitchen sink. Then, place a dishmat in the bottom of the sink to protect the dishes from possible damage. Place the melamine dishes in the sink. Add a squirt of mild dishwashing liquid. Don't use chlorine-based detergents because they can fade the color of melamine dishes.
Fill the sink with warm water. Wash the dishes with a dish cloth, but don't use scouring powder on melamine as it can scratch it.
Rinse the clean dishes thoroughly with warm water. Place them in a dish drainer to air-dry, or hand dry them with a dish towel. Either drying method works equally well.