OK, so yesterday we went through the prep work needed before you start painting kitchen cabinetry. Every surface you just prepped needs to be primed now. You cannot skip this step or you will end up with a top coat that will peel off within weeks of your completing all of this work. That's bad.
I recommend that people use an oil-based epoxy primer called Kilz. Kilz was developed as a paint for bathtubs originally, and there is little it won't stick to. Be sure to use the original, solvent-based formula. There is a water-based companion product out there called Kilz 2, but I don't trust it. The water-based stuff is great for hiding stains on walls, but you need something with the staying power of the original.
I prefer that the primer be applied with a 4" roller with a 1/4" nap. Do not skimp on the rollers, you want a lint-free roller and for me, they are made exclusively by the Purdy corporation. Buy good tools! I cannot repeat that often enough. You will find Purdy painting supplies at Sherwin-Williams and at Home Depot.
I'm telling you to use a short roller because I don't like to see brush marks on cabinetry. The four-inch size will allow you greater flexibility when you're priming and later, painting. Use the primer sparingly, it's better to go to light than to go too heavy. So prime everything and let it dry. This will take a while. Pay attention as you're using that Kilz too. It will stick fast to everything it touches, including skin and it's a bitch to remove.
When the primer's dry, inspect everything to be sure that everything you've primed has been covered with an even coat. Sand down any gloppy areas and remove the dust with a tack cloth.
You want to paint your doors and cabinets with a high-quality, exterior paint. Exterior paint is more resilient than wall paint. Avoid using anything shinier than an eggshell finish. The shinier a paint finish, the more flaws it will show. You cannot replicate the look of sleek and shiny European cabinetry, so don't try. The closer to matte sheen paint you use, the better your finished product will look.
Apply your paint in even strokes with a short, 1/4" nap roller. Go light on the paint. Paint everything and let it dry. Once it's dry, go back and sand down any raised areas. remove the dust with a tack cloth.
Paint everything with a second coat. Take your time. Once the second coat is dry, look over everything again and make sure that you have smooth, even coverage. Depending on what you painted over, you may need to apply a third coat of paint.
Oh, please resist the temptation to get cute with your finish. Faux finishes have no business on kitchen cabinetry and now is not the time to try out something you saw in a magazine. Paint a canvas and hang it in your kitchen if you can't help yourself. Cheap fixes are supposed to retreat into the background. Something like this will stick out like a sore thumb and end up scaring away your guests. Don't do it!
Once everything is painted and dry (this will take a good day or so), you can begin reassembling your kitchen. Go slowly, take your time putting everything back together. Once the doors and drawers are back in place, attach all of the knobs and pulls.
Taaa daaaa! You're done. You may now curse the day you thought it would be a good idea to paint these cabinets.