Experts and BHG readers answer.
Some trees, like mulberries and maples, are water- and nutrient-hogs and plants generally won't thrive beneath them. Bulbs are a good solution if you want color; their shallow roots won't compete with deciduous trees. Try groundcovers for shade, like Ajuga and lungwort (Pulmonaria). If you can grow Hostas, you should be able to grow Astilbes. They like conditions evenly moist and the soil a bit richer in organic matter. If they don't thrive in the ground, try containers. Dry-shade lovers with interesting foliage and some flowers include Lamium maculatum (Dead Nettle) and Lamiastrum galeobdolon (Yellow Archangel).