Normally after 3 years old can say if the kids has asthma or not. The age around 2-3 years old is a 'grey' area. Only depends on kid's past medical history to make diagnosis.
The treatment for asthma is called Ventolin-the puff (to release the symptom). If the condition gets worse, the doctor may prescribe a regular medication for prevention.
Doctor says kids may total recover when s/he grow up. Prevention is more important. You may observe if there is any trigger to cause your kid any symptoms. Like dust, smoke, animal's fur, infection, etc. Try to avoid those triggers.