Asthma is an allergy and is triggered by something. The best non medication treatment for asthma is learning your triggers and avoiding them. Common triggers are smoke, dust, mold, mildew, plants, dust mites, pets and grass/weeds.
If you can not figure our your triggers, you may need to see an allergist and have allergy screening done. This may point out your triggers.
The National Asthma Prevention Program and the Expert Panel of Diagnosis and Management of Asthma both agree if you have to use a prescription inhaler such as albuterol more then two time per week, your asthma is NOT in control and you will need a prescription controller medication.
Controller medications are steroids (Asthmacort Asthmanex, Flovent, Pulmocort), Leukotriene modifier (Singulair, Aculade, Zyflo) or mast cell stabilizers (Cromolyn sodium, Intal, Tilade).
You may want to talk to your doctor about several strong controller medications and maybe Xolair shots.
If you want a proven, all-natural way to cure your asthma, without having to pay for useless medications with harmful side-effects, then this is the most important page you'll ever read.