Initially you have to sit on your backyard with a beverage or good book, relax, and watch the sun go round, taking note which areas are in full shade and for how long, or dappled shade at what times etc. You can then match plants that tolerate certain amounts of shade with appropriate locations.
Hosta or Plantain Lily
The classic ground cover perennial for full or part shade. Fully hardy, they will thrive in a rich moist neutral soil offering clumps of attractive foliage. Varying in size from the compact to the very vigorous, many produce elegant flower spikes in mid-summer. The partial shade loving 'Gold Standard' has violet flowers and foliage that turns from green to gold in the summer. With a spread of up to 4ft the 'August Lily' (H. plantaginea) prefers little or no sun and has the most fragrant white flowers in late summer above glossy green leaves. 'Thomas Hogg' with pale violet flowers will do well under a tree canopy.
Another clump forming perennial with striking foliage and tall spiky flowers. They will tolerate a moist semi-shaded environment. 'Gregynog Gold' has heart shaped deep green foliage and orange/yellow flowers from mid-summer. 'Desdemona' is also fully hardy with leathery leaves and vibrant orange flowers. L. przewalskii will be a delight with spires of mustard yellow towering over its dark green leaves.
Preferring shade or semi-shade mahonias are evergreens with yellow fragrant flowers and offer good ground cover. 'Heterophylla' grows to about 3ft with a 5ft spread, has reddish shoots, bright green leaves that turn red / purple in the winter and spring flowers. Also spring flowering, the holly like leaves of 'Undulata' will bronze in the autumn. Mahonia x media 'Buckland' bears fragrant autumn flowers that will last through to early spring as does 'Charity' and other hybrids.
Rhododendron / Azalea
Natural woodland shrubs that like dappled shade and a neutral – acid soil. In a sheltered position their colourful flowers will light up any shady area. Varieties are many and various including compact hybrids suitable for a small garden such as 'Hexe' with striking crimson blooms, 'Curlew' that has funnel shaped yellow flowers, the crimson / purple 'Hatsugiri', 'Alison Johnson' with bell like pink flowers and the white flowering 'Palestrina'.
In a fertile shaded area these evergreen spring flowering shrubs have aromatic foliage and attractive berries. S. japonica subsp. Reevesiana has dark green leaves tapered to about 4ins. and will produce fragrant white flowers followed by red autumn berries. S. Japonica 'Fructo-albo' carries white berries but will need a male plant close by for pollination, perhaps Skimmia × confusa 'Kew Green' which has creamy flowers in April and May.
Dicentra or Bleeding Heart
Fully hardy perennials that do best in semi-shade moist conditions. 'Spring Morning' is small (12ins) plant with grey / green fern like foliage and arching sprays of heart shaped pink flowers. 'Stuart Boothman' is a slightly larger variety with similar flowers and foliage while spectabilis 'Alba' or White Bleeding Heart spreads to around 2ft and has sprays of exquisite white flowers in late spring and summer.
Hardy Geraniums will grow in most soils and are particulalry useful in dry shade. G. phaeum is known as the 'Mourning Widow' with purple / black flowers in the spring. 'Bevan's Variety' is another that does well in dry shade, this semi evergreen cereates a mat of aromatic leaves with purple / pink flowers. Another attractive lilac pink flowered ground cover variety is the Knotted crane's bill (G. nodosum).
These perennials love the shade and are grown for their beautiful pendant flowers and attractive marbled leaves. They also flower late, so extending the season's colour. C. hederifolium will grow almost anywhere with its pinky white flowers. C. purpurascens is harder to grow and needs a little more moisture but you will be rewarded with the most fragrant pink / reddish purple flowers right up to Christmas. Following on, the maroon and white flowers of C. coum 'Album' start to appear in January above its deep green leaves.
There are many cultivars suited to full or partial shade, too many to mention here. The early summer flowering P. sieboldii (white, pink and purple) and P. polyneura (pink /purple) will both tolerate full or partial shade, P. verticillata has fragrant yellow flowers and is happy in partial shade along with P. reidii with its pure white clusters in early summer. The many others, tolerant of partial shade and full sun as long as the soil remains moist include 'David Green', 'Garryarde Guinevere' and 'Tawny Port' that has wine coloured flowers in the spring.
Guaranteeing autumn interest with their deeply beautiful foliage and ornamental bark, Acers will tolerate partial shade in neutral to acid soil. Following clusters of red / purple spring flowers, the leaves of the Japanese Maple turn a magnificent red in the autumn, while the Vine Maple's leaves transform into brilliant orange. Bear in mind though that Acers can grow into sizable trees and may not suitable for a small garden.
Finally if you have a wall that is partially shaded and need a climber, there are several that while not feeling totally at home, will tolerate some shade. These include Boston and English Ivy, Virginia Creeper, Honeysuckles that match interesting foliage with fragrant flowers, and even clematises such as 'Carnaby', 'Nelly Moser' and Marie Boisselot'.