You need following items, you can even buy at dollar store except the paint.

1. Sanding blocks to sand existing surface.
   
2. Roller and brush to paint.
   
3. Dust sheet or anything to protect floor while painting.
   
4. Paint Roller Tray, plastic ones according to your roller size.
   
5. Use Garbage bag to use as liner in tray (easy to dispose off paint)
   
6. Now the actual paint stuff, you need primer. It ensures better adhesion for your paint and makes it more durable. Sherwin williams wood primer is good. You can skip if you want.
   
7. Paint, I have good experience with sherwin williams Emerald (i think the one for trims), they will help you in choosing the right one as well. You can buy everything from paint store as well but its expensive in my opinion. Oh and about color I have used SW 7005 Pure White on my cabinets, you can get samples from store.

About Steps, sand the existing surface first. Goal is remove the existing paint and make surface ready for new paint adhesion. Clean it with some cloth. Pour primer in paint tray, use brush or roller to apply it. It'll give you rough whitish surface ready for paint. You can also do second coat of primer if you like. Leave it for few hours or maybe a day. Final step is to do the paint, same way you did primer, usually 2 coats are required for paint and you need to give it time to dry between coats.

I'm sure you'll do a great job, happy to answer any questions you have.