When doing over a kitchen discolored from cooking grease and smoke, cleaning is step number one. This is obvious, but often is not done correctly, due to the unpleasantness of the task. Wiping down all surfaces, walls/woodwork/and ceilings, with a sanding deglosser probably works best. The volatile odor and vapors may be a problem for access or health reasons, so any "green" cleaner will have to do in such cases. Just be sure to clean as much buildup as possible from the surface to be repainted. Once this is completed, scuff sanding of enamel-painted trim or walls should be done next. Scuff sanding means a brief roughing up of old finish, not a thorough sanding. The painting term "give the surface a tooth" is what you are looking for. This allows new coating to hold on the old paint and not flake or chip off when bumped against. An alternate to scuff sanding is to use a sanding liquid/ deglosser, as mentioned earlier. One brand is called Wilbond, which gets rubbed on the surface and must be painted within 30 minutes of applying. This limits the size of the work area but if you can stand the smell, the job will go faster. Especially since after sanding you need to deal with the dust. So sanding and then wiping away the excess with a Wilbond type product would also work and you wouldn't have to be concerned with the 30 minute time limit.
 Priming all and any bare wood with a good "enamel underbody " or universal primer is necessary. Doing an entire primer coat may be needed depending on the condition of old coating, or if a drastic color change is being done. There are so many good primers/ underbodies that you should use common sense and pay for quality, and not skimp. Most of the time one coat is all that is really needed for going over paint. But if going over stained/polyurethaned surfaces, you probably could use two. And a shellac based primer over polyu  works well, such as Zinsser BIN primer. Using a small roller with a screen that fits into a gallon can is a good way to coat cabinet doorfronts, door panels, and uneven woodwork. But always keep a brush handy to even out any rolled on paint to assure a smooth finish, especially with enamel paints.
 Finish coating with quality enamel paint (Benjamin Moore- Satin Impervo- oil base or waterborn), is worth paying for. This paint is more expensive than home improvement brands, but is, in my opinion, worth the money. Of course, doing the necessary preparation is the most important part of the job, but a quality paint will last years longer and make the prep down the road that much easier. Doing two coats will ensure both a uniform color and durable finish. Once again, using the little "whizz" rollers really does speed up the tedious job of painting your kitchen walls and or woodwork. Hope this helps you out!