How to get rid of anxiety without medication?

Anxiety is primarily due to the sense of uncertainty about the future.  The uncertainty may arise either because of the sense of inadequacy within or the enormity of the world around us. This is the root.

How are we to get rid of this? By constantly reminding ourselves that in our origin and essence we are not small, limited, helpless creatures but a portion of the Divine.  If that is difficult, then anything that can help us give the sense of the Divine Power is good, for example prayers.

You can also divert the mind from anxious foreboding through work and games. Games especially help build confidence by increasing the secretion of endorphins. Calming methods such as deep breathing, mantra, music, calling peace are all helpful in anxiety management.

A simple practice is to step back and see the relative importance of the events and circumstances that we anticipate and get worried about.

Regular practice of asanas and especially deep relaxation with or without imagery can be one of the most effective means of eventually saying goodbye to anxiety.