What can you actually grow in a shady garden?
A great deal — provided you first establish what kind of shade you have, because the word covers conditions that are completely different from a plant's point of view.
The distinctions that matter:
Dappled or light shade — under a high open canopy, with moving light through the day. The easiest condition in the garden, and many plants prefer it to full sun.
Partial shade — direct sun for part of the day. Whether it is morning or afternoon sun changes what will grow, since afternoon sun is hotter and harsher.
Full shade, moist — north-facing, open to the sky, no direct sun. Genuinely productive, and far better than its reputation.
Dry shade — under trees and against walls, where roots take both light and water. This is the difficult one, and it is what most people actually mean when they say nothing grows.
Deep shade — narrow side returns and dense evergreens, where honest options are limited.
What to do about dry shade specifically, since it defeats most attempts:
Improve the soil substantially before planting, with organic matter, and mulch annually.
Plant small, since small plants establish where large ones fail against established roots.
Plant in autumn or early spring and water through the first two summers — establishment is the whole battle.
Consider raising the tree canopy to let in light and rain.
What actually performs:
Moist shade — hosta, fern, astilbe, brunnera, hydrangea, hellebore, pulmonaria, tiarella.
Dry shade — epimedium, euphorbia amygdaloides var. robbiae, geranium macrorrhizum, vinca, dryopteris, cyclamen hederifolium, ivy.
Spring bulbs, which flower before the canopy closes and are the single best use of ground under deciduous trees.
Structure and foliage. Shade gardens work through leaf shape, texture and contrast rather than flower colour, and the good ones lean into that.
Pale colours and variegation lift a dark area, since white and cream read at low light far better than dark reds and purples, which disappear.
Reflected light from a pale wall or a mirror makes a genuine difference.