This is a tricky question. If the shady area is completely dominated by a house, other building or a tree or a wall which blocks out all natural light then the answer will be different to a normal garden which has a sunny area and an area where there is less or no sun at all, but still has a lot of natural light.
Most plants will grow in a garden where there is natural light providing the soil is the "right" one, even if this area is shady. If you have a dominant tree which stops or restricts natural light, then you can still do somethings which will improve the chances of growing more plants. For eg. can some of the tree branches be cut back? or can some of the branches be thinned out?. Next if there are tree or other roots within your shady patch you will need to drastically improve the soil. This can be easily done by adding compost or manure to enrich the soil. A healthy soil will allow a greater number of plants to be grown even if the light is poor.
I would start by finding out the ph level of the soil in the shady area. This is very easy to do. Secondly, improve the soil that is already there by using a compost or manure. Dig this well into the soil. Thirdly, evergreen shrubs and bushes don't normally require very much assistance to get them going. Place one or two to structure the area. Look for plants that do well in woods, or will grow with poor light. If the plants natural habitat is dark or poorly positioned, then the chances of you being able to grow them at home will be greatly improved.
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