Through logical processing of my emotions. I know some people think it's impossible, but I find it rather easy. I wage a logic war with my emotion, debunking any irrational fear with the best argument I can come up with.
I usually win.
That said, there are times when you should be legitimately anxious. Assuming you're not overreacting, anxiety is our body's signal to be more alert, more observant. If you're anxious because a stranger is following you, that isn't one of the times you should 'calm your nerves.'
The most common anxiety-producers are speech-making and direct conversation with other people. In those cases, practice convincing yourself the reality of the situation, rather than what you believe is happening.