Remove any existing paint or varnish from the item using either sandpaper or an electric sander. It's very important that you get it completely smooth so there are no splinters that could hurt the baby. If sanding by hand, you need to first use rough-grit sandpaper to remove the existing paint or varnish, and then use a fine-grit one to get the smoothest finish.
Apply a coat of low-toxicity wood primer using a paintbrush. Paint only one coat using even, downward strokes. This will create an even base for the paint to go on. Allow it to dry for the time specified on the package directions before moving on to Step 3.
Paint the furniture in any color of your choice. You can go for the traditional pink for a girl or blue for a boy, or you can try something more neutral, like cream or beige. Look for zero volatile organic compound or low VOC paints, as these are the least toxic.
Apply more coats of paint, if necessary, by repeating Step 3. Once you can no longer see the grain of the wood beneath the paint, then you have enough coats on your furniture.
Decorate the furniture, either with stencils or by painting freehand if you're artistically inclined. Skip this step if you just want the furniture painted a solid color.