Control the ant population attracted by the honeydew to allow activity by natural predators. Apply narrow range oil during the dormant season. It is difficult to control due to the tubers beneath the soil. Pull out the plants by hand or hand-hoe deeply to remove the whole plant. Tubers may re-sprout but will eventually weaken, so continue to manually remove.
Planting competing plants nearby can help by shading the nutsedge, which needs sun to thrive.
Pre-emergence herbicides will also provide limited control. In general, limit lawn areas or replace lawn with water conserving ground cover or hardscape. Group plants with similar irrigation requirements. Use drip irrigation wherever possible and mulch to conserve soil moisture. There are a number of gardening books dealing with water conserving planting, including Ortho s Gardening in Dry Climates and HP Book s Plants for Dry Climates which contain plant photos, descriptions, and culture.