What causes an anxiety disorder to develop, and how can I control it without drugs?

Causes vary from. reacting to stressful situations and not processing them at the time to possible physiological predisdositions ( hereditary or familial modeling). Psychotherapy can help you become less anxious.. A therapist can teach you relaxation techniques & talk about the things that make you anxious. Together you can learn different ways to cope with what is causing your anxiety.
Anxiety happens. when your mind registers a threatening or intimidating future event & your body prepares for action (fight/flight). You can change your thoughts about the triggering situation, learn to calm your body's reaction, or deal with the situation to make it less threatening. Talk to a psychologist or counselor who treats anxiety. Biofeedback can help -- www.bcia.org & www.aapb.org.
Awareness. Anxiety develops when we lose awareness of our thought and feelings. Before we realize what's happened, our body is responding to a situation with high anxiety and we don't know why. Mindfulness based stress reduction this can help slow your thoughts and bring you back to the present moment in a peaceful way. I recommend the book the mindful way through anxiety by susan orsillo. Good luck.
Anxiety treatment. Anxiety develops both biologically and through learned behaviors. While research shows that the best treatment is a combination of drugs and therapy, there are some things you can do to help. Proper sleep hygiene, diet, and exercise are critical. You may also benefit from talk therapy where you learn relaxation training skills and cognitive restructuring.
Revise thoughts. There are a dozen or more anxiety disorders, and they all have different causes. Learning as well as biological factors certainly play important roles. Most anxiety disorders are accompanied by particular types of thoughts that exacerbate the problem. Therapy helps one identify and revise dysfunctional thoughts and behavior to decrease anxiety symptoms. Early treatment is always better.