Summarize:

Use a paintbrush to apply a primer that is specifically for melamine. Target all of the areas that you cannot easily reach with a roller. Primers that are specifically for laminate wood are an alternative option. Roll the primer in one direction across each surface. Ensure that the roller always sounds crinkly and wet, and if it loses that sound, apply more primer. If you are using a new roller cover that has fibers, wrap it in masking tape before you use it. Rip off the masking tape to remove any loose fibers that would have otherwise been stuck to your project. Use 220 grit sandpaper to smooth over any drips or other marks caused by the primer. Wipe over the sanded surfaces with a tack cloth again. The instructions that are on the primer will indicate how long it will take to dry. This normally takes around 4 hours. Cover the full surface of the kitchen cupboards or furniture again. Wait for the primer to dry. You don't need to sand the surface again after the second coat of primer, unless you notice more bumps or imperfections. Use a foam roller to evenly coat all surfaces with paint. Let the first coat dry for 6-8 hours. If you prefer to use a paint brush, brush against the grain first and then brush with it. Paint applied to melamine takes longer to dry than on wood. This is because melamine isn't as absorbent. You can buy paint specifically for melamine surfaces from home improvement stores. Use either a foam roller or paintbrush again to apply paint to all of the surfaces. Let the final coat dry for 24 hours. Start with the back or inside of any doors to cupboards, so that you can get used to spray painting there first. Then spray paint your entire project, and let it dry overnight. Wear a respirator mask at all times when working with spray paint. Check that the spray paint can be used on melamine surfaces by reading the label before you purchase it. Apply a second coat with spray paint if you need to once the first coat is dry.
Apply primer with a paintbrush over all of the edges and corners. Use a roller to apply the primer to the whole project. Sand the primer once it's dry to remove any imperfections. Add a second coat of primer. Apply the first coat of melamine paint over the primed surfaces. Add the second coat of melamine paint once the first is dry. Spray paint your project if you prefer a smoother finished surface.