What is the best way to manage asthma in children ages 4-9years old? Also would a specific diet be required?

Varies. Asthma is a disorder of variable intensity and trigger factors. It can vary from unrecognized to chronic and life threatening. Each patient must be evaluated and treated based on their individual findings. No two patients have responded exactly the same to any treatment.As such, it is unrealistic to list a "best" medication or plan.Find what works and keep track of triggers ; a written action plan.
Depends. It depends on the severity of asthma. It could range from only intermittent albuterol for mild intermittent, to needing increased amounts of inhaled steroids plus/minus leukotriene inhibitors. I am not aware of any diet specific to asthma although one thing to keep in mind is that people with asthma concurrenty may have environmental or food allergies.