Plan the Molding
If you want to embellish the cabinets with some molding, you will need to decide on both the style and size. Thin, flat molding will suit most design plans just fine. Lattice and screen molding are the most likely choices. Both are about 1/4-inch thick. Screen molding is usually 3/4-inch wide, while lattice can be found in widths between 1 1/8 and 1 3/4 inches. If you are not sure how you would like to arrange the molding, buy strips of each size you can find, take them home, and play with several different arrangements. Once you find a design you like, prime and paint the molding before you start cutting it up.
Molding will only look good on a door frame if the corners are mitered. Plan to buy or borrow a power miter saw or, if that is too much trouble and expense, a decent miter box to use with a handsaw.
Prepare for Painting
If you try to paint over melamine without proper preparation, you will almost certainly be disappointed with the results. Professional painters will tell you that the biggest part of their job is preparation, and that attitude is definitely required for this type of project. First, remove all cabinet doors and drawers and take them to a room where they can be painted and left to dry undisturbed.
Kitchen cabinets are often coated with a layer of grease, and grease does not mix well with paint. So begin by scrubbing all surfaces with a strong detergent, and then rinsing thoroughly. Trisodium phosphate (TSP) is an old standby for this purpose, but be sure to use it exactly as directed (including the part about wearing gloves and eye protection).
After everything has dried, use some medium-grit sandpaper to scuff up the glossy surface and remove any bumps. Then wipe the surface with a tack cloth.