What is the best way to handle anxiety without taking medication?

Many, pick a winner! Many types of psychotherapists have methods to treat anxiety without medication. Read about them, inquire what they do - take a test drive to see if you feel comfortable with the approach and then stick to it for long enough to help it work. It might be hard at times, but if you can meet the challenge, you can succeed. Mindfulness meditation helps many, so do other cbt approaches. Good luck!
Depends on impact. Anxiety is normal, necessary for awareness of self & environment. It's a disorder if it causes distress or impairs function. The relaxation & stress reduction workbook by davis, eschelman, & mckay is excellent. Seek therapist trained in anxiety management. Breathing, visualization, progressive muscle relaxation, mindfulness, & cognitive behavior therapies are powerful. Relax & enjoy the challenge!