What a HUGE question!! Honestly, asthma management is a huge area, and this is best addressed by either your GP or a pulmonologist. Treatment of asthma really depends on the age of the patient and the severity of the asthma.
In general though, we group asthma medications according to their actions. The two major groups of medications in asthma are relievers and preventers. Relievers are used to manage symptoms as they arise, and include the trusty ventolin inhaler. These meds are used when someone has an acute episode of asthma, with wheeze and shortness of breath. The dose depends on age and severity and should be discussed with a physician.
If the asthma is more severe, and the reliever (ventolin) is required more than once a fortnight or so, then your physician may decide that a preventer is necessary. These meds include flixatide (fluticasone) and other inhaled corticosteroids which act to reduce the overall number of asthma attacks. It is important to note that while ventolin is only used when needed, reliever meds must be taken every day to have an effect.
There are many other drugs, including things like salmeterol and montelukast, but these are really beyond the scope of this discussion, and should be discussed with your physician. Hopefully this helps!
Aj :)