For our oak cabinets, I started by removing all of the drawers and doors, and as I did that, I labelled them so I knew which piece belonged with which part of the built-in units.
I then prepped all of the wood with Krud Krutter (not just the stuff meant for cleaning - they have product that specifically meant for paint prep).
After it dried, I filled in the wood grain with putty and sanded it smooth (you really only have to do this if you have oak cabinets because the grain is so deep. You also don't have to do this if you don't mind the grain showing through the new paint).
Next, I used a paint sprayer to cover everything with a solid layer of primer (Behr has product designed specifically for cabinets). After drying, I used the sprayer to add a couple coats of my final paint colour (again, Behr has awesome, enamel-based product for this type of project).
Once again, I let everything dry and then put each piece back in its original place.
I also cleaned and spray painted the original hardware to give it a fresh, modern look, which helped us save money (brand new hardware can be expensive depending on the size of you kitchen)!
I hope this helps.
If you don't have access to a sprayer, you can definitely use regular brushes and rollers! I'd suggest foam for the rollers.
For kitchen cabinets, remove all hardware, drawers and doors, Mark on back where they go. Wash down with TSP and then sand the sheen off. Prime with oil based primer, lightly sand again if not smooth, paint 2 coats of oil based paint.
You can do the same with your furniture.
How to Paint Cabinets
Make sure they are clean and dry. Remove the doors and hardware. Mark the doors and cabinets with tape where they go. Lightly sand the doors and cabinets to remove any gloss and roughen the surface for paint with 100 grit sandpaper or a green Scotch Brite pad.. Use a tack cloth or damp rag to remove dust after sanding. Prime with a stain blocking primer like KILZ. Acrylic or water base paints are low-fume and clean up easily with water. Alkyd or oil-based paints require good ventilation because the paint contains solvents that can irritate your lungs and make you feel sick. Alkyd options require mineral spirits for cleanup, but they provide a hard, durable paint finish. Whichever you use, buy the best-quality paint you can afford for a lasting kitchen cabinet finish. Seal with at least three coats with a water based polyurethane. Use a small foam roller and foam brush for a smooth finish.
Same process for the bedroom set.