Mow your lawn beginning in spring, to keep it neat. Continue to mow the lawn regularly thereafter, mowing before the grass grows to a height of 2 inches.
Nurture your grass by watering it with 1 inch of water per week, unless you receive enough rainfall that week to skip it.
Fertilize your lawn to keep it healthy, beginning in May and continuing through August. The University of Missouri suggests using 2 lb. of nitrogen per 1,000 square feet over those four months, which breaks down to 1/2 lb. per month. Scatter dry fertilizer over your lawn and water to work the nutrients into your soil. Use a balanced lawn fertilizer.
Manually weed your lawn to remove competing grasses and other weeds. If you need help, use herbicide spray to kill the competing grass, then pull it out.
Rake your zoysia if it becomes thatched or matted. Use a metal grass rake and rake back and forth over the tangles, just like you would de-tangle your hair.
Apply one more dose of fertilizer in August, and then stop fertilizing until spring. Stop mowing in the late fall when your lawn goes dormant.
Continue to water zoysia periodically when it is dormant. Water on warm or windy days. When the grass begins to grow again in the spring, resume your care program.