I was not fond of the original hardware, so I removed it and purchased these cute flower drawer-pulls from Coco and Toulouse Go Shopping, another of my favorite little shops in Sellwood.
To go from two holes in the front of each drawer to one, I filled in the existing holes with Elmer's Carpenter's Wood Filler, which my dad recommended to me. Once it's dried and sanded flat, you can paint over the wood filler and it will be indistinguishable from the rest of the drawer.
Next I covered the entire piece of furniture, including the insides of the drawers, with some primer that my parents had leftover from painting their house. When changing from a dark color to a much lighter color, primer makes it so you don't need as many coats of paint. It also seals unfinished wood so that you can paint it. Since I was going from black to white, I still had to use a couple coats of primer, but I would have needed a lot more paint if I had not used the primer.
After the primer, I very carefully measured to the center of each drawer and drilled a hole just big enough for my new drawer pulls to screw into. I measured from each side of the drawer front in order to get the hole in the exact center so that it wouldn't be unbalanced.
Next, I painted over the primer with white gloss spray paint from my local hardware store, after first promising not to use it for graffiti.
Once the white paint was dry, I used some painters tape to outline all of the places that I wanted to be a different color, in the hope of making straighter lines. I then filled in those areas using a small paintbrush and some pink acrylic paint. Some of the pink paint leaked under the tape so I had to touch up the lines with more white paint. Be careful doing this part because it your touch-up paint isn't exactly the same color as the main paint you used, it can be a problem.