How can I distress a cupboard made of melamine

Here is an article that might help - http://homeguides.sfgate.com/distress-painted-laminate-furniture-91031.html

Cover with something else and distress it. You really DON'T want distressed melamine. Trust me!

https://www.pinterest.com/pin/332984966169528597/?lp=true

You can distress anything using a laying paint method. Just choose the colors you want such as brown, white, and teal. Paint the brown, let dry, then dry brush some white on top and then dry brush the teal. Repeat the process very lightly over and over until you achieve the look you want. Lightly sand with fine sand paper in between the coats of paint. Layering very light paint and showing the brush marks. Here is a bench (that I made from a bed headboard and footboard) that I did using this technique.