If they are inexpensive, these small - and large - pieces of furniture often have a pitiful appearance. The first operation will therefore consist of a very serious cleaning. As the metal support is not very interesting, you will have to achieve a uniform background ... which implies a good repair.
The step by step
Cleaning and pickling
Disassemble everything that can be: doors, shelves, and take out the drawers.
Wash all of this with a mixture of cold water and Saint-Marc detergent at the rate of 100 to 150 g per liter of water. Rinse thoroughly with warm water. Let it dry well.
If the paint is damaged, strip it using a gel that you will pass on all visible surfaces with a nylon brush. Leave to act according to the manufacturer's instructions, then, when the paint blisters and softens, remove the old layers with a spatula. If some areas resist, try the operation again.
Once the surface is clean and free of its old paints, you will often need to perfect it to make it completely smooth. To do this, use a small electric sander and special metal sandpaper if necessary.