For a sloped backyard, you'll need to take an additional factor into consideration when selecting plants. Aside from the sunlight and soil needs of various species, a sloped lawn will most likely mean that some areas of your garden are extremely well-drained, while others receive an extra measure of irrigation. Before you start planting, test the soil moisture at the highest and lowest parts of the garden. If you notice a sharp gradient, consult with your local horticultural extension about plants that are well-suited to your location that do well in relatively marshy and arid locations. For very steep slopes, plant sprawling ground covers, which will help protect against erosion.
You can introduce many design features into a sloped yard that will enhance its beauty as well as the health of its plants. To make use of the low-lying section at the foot of a steep slope, install a "dry river" of decorative stones or rocks. This eliminates the issue of finding a plant well-suited to this damp area. For a variation on the same principle, install flagstone pavers over porous gravel for a functional walk or patio surface. It will cut down on runoff, compared with impermeable hardscaping.
To avoid the complications associated with a sloped yard, you can circumvent them entirely by building a series of terraces. Think of a sloped yard as a ramp and terraces as a series of shallow steps. If necessary, use bricks or stones to build short retaining walls for each terrace. How you divide the yard into terraced levels will help define its various spaces, such as a sitting area, a dedicated vegetable patch or a rock garden.
For a practical variation on the "dry river" element, dig out the bottom of your "river bed" at a slight slope, approximately 1 to 3 degrees. Orient this trench so it drains into an outlet at one end. Fill it with stones or rocks, just as for the "dry river" design. Known as a French drain, this element will help to balance the moisture level in various parts of the yard and relieve any waterlogged low-lying areas.