Keep new zoysia lawns moist until they've established good roots. You can determine root establishment by tugging on a small area; if it comes up easily, then roots have not yet established.
Mow your zoysia grass whenever it reaches a height of 2 inches. Mow it down to 1 ½ inches high, and no lower than ¾ an inch.
Apply a zoysia-specific fertilizer containing pre-emergent weed killer in the early spring, just as the grass starts greening up and before weeds start growing. Use the amount indicated on the label for the size of your lawn.
Fertilize zoysia during the summer months only if it shows signs of nutrient depletion. These signs include color fade all over the lawn.
Give your zoysia lawn at least 1 inch of water per week. If the weather is hot and dry, you may need to give more water than this. Give extra water if grass blades start curling.
Fertilize zoysia in the autumn again with a zoysia-specific fertilizer containing weed control.
Dethatch the lawn when old grass appears compacted and you can no longer see soil between clumps of grass. Dethatch using a rented machine from a garden center and before the grass greens up in the spring.