Symptoms of ozone exposure in healthy people include coughing, wheezing, and pain when taking a deep breath. Studies show that children don't usually report symptoms even when they have measurable decreases in lung function.
Children with asthma are more likely to have symptoms of their disease the evening or next day after exposure. That is because it takes a while for inflammation of the airways to get going (much like a sunburn, which is worse that night or the next day). Healthy children are not likely to have serious effects from a single exposure to high ozone levels. However, aggravation of asthma can be more serious, leading to effects such as increased medication use and visits to health care providers, including emergency rooms.
Less is known about the effects of long-term exposure, but reducing exposure on days when ozone levels are high will help. The actual "dose" of ozone received is dependent not only on the concentration of ozone in the ambient air, but also on activity levels and the duration of the exposure.
For more on the health effects of ozone, please see http://www.epa.gov/air/ozonepollution/health.html