The smell of urine in your grass is caused by concentrated nitrogen that soaks into the soil. Although both male and female dogs can cause this smell, females tend to cause bigger problems because they urinate all at once on a specific spot, releasing larger quantities of urine -- and thus creating a stronger smell. Cleaning up the smell might seem difficult, but some water and a few tools will do the trick.
Wash It Off
Perhaps not surprisingly, your first tool for attacking urine odor is plain water. The odor and the dead, brown spots caused by a dog urinating on your lawn can be minimized by irrigating the area with plenty of water.
For better results, try watering the area right after your dog urinates on the grass, as this will help dilute the urine faster and before it soaks into the ground and causes the odor. If it's too late for that, you can still "wash off" the grass by adding about three times as much water as the amount of urine you estimate is in the grass. Don't worry about overwatering, especially if this is something you do infrequently. The grass will not suffer from too much water once in a while.
Try Crushed Lime
Too much lime can damage healthy grass, so apply only to brown areas. Lime can last for years when applied, but you might need more frequent applications if your lawn is damaged. You can buy testing kits to confirm the acidity of the soil and see if more applications are needed.
Preventing the Smell
The best thing you can do to prevent urine smell is to redirect your dog to urinate somewhere else. For example, you can create a special potty area in a corner of the yard. Spread gravel or mulch in the area and either replace it regularly or wash it off to prevent smells.
If you can't prevent your dog from urinating on the grass, you can make sure your dog is getting enough water, as this can help dilute the harmful chemicals in the urine. Provide plenty of fresh water or try adding some warm water to dry food so your dog consumes more liquid on a regular basis.