In most traditional designs, symmetry is very important when landscaping. Things often match from one side of the property to the other. Yards that aren't mirror images of each other still usually have off-setting features to provide balance. A more abstract look strives for, and achieves, asymmetry in opposition to the traditional balance of more reserved landscaping styles. This includes ideas such as having a large feature, such as a flower bed or water feature, on one side of the yard with no balancing feature on the other.
One interesting way to create an abstract feel to your garden is to think in terms of geometry, rather than in terms of how a yard should look. Think of interesting shapes or angles, whether triangles, squares or even more complex shapes, and then think of ways you can create them with your landscaping elements. You have the shapes of flower beds, lawns, paths, furniture, hedges and more to experiment with in the creation of abstract shapes.
Another way to add a large abstract touch to the yard is to add in some additional features or pieces designed in an abstract way. Many yards feature a boring piece of traditional statuary, a bird feeder or a fountain of some kind. Buck the trends in this area and instead opt for a piece of modern art or outdoor abstract sculpture in the yard. These pieces are unusual enough that they should immediately draw the eye and create interest in your landscape.
As with anything that is said to be in the abstract style, color holds the potential to add much to an abstractly landscaped yard. Look to legitimate abstract art for inspiration. See how color is used randomly and in off-balanced and shocking ways. Think about those themes when seeding plants, growing flowers, installing features or choosing materials to use in your yard.