Wikipedia contains this sentence inside the definition of shyness:
`The primary defining characteristic of shyness is a largely ego-driven fear of what other people will think of a person’s behavior.`
Your question feels sensible, because you don’t want to destroy shyness, you want to reduce it. But I will be honest with myself and to you. I feel I know the answer to your question of how to reduce shyness, but to destroy shyness completely, is a road I haven’t walked myself fully yet. So, even though your question felt sensible the first time I read it, I feel you won’t want to stay even at the reduced shyness level once you reach it. I have reached it, and I want to go further. To destroy shyness completely.
That being said and I will also include why I said it in this answer, I will try to dissect shyness into two parts.
The first part is the fear of being judged by others. This fear leads us to feel unloved, unable to feel love once we are judged by others. To be unable to feel love is the greatest cause of feeling unhappy. In fact it is the deepest and sole cause. So shyness is a subconscious strategy we utilize to block ourselves from entering into situations where people will judge us (explicitly, by directly showing it or implicitly by implying it in their actions)
The second one is the fear of being harmed by others. Harm means here that our survival is threatened. This part of shyness is a direct survival strategy to preserve ourselves from entering scenarios in which we think that people would harm us.
So how to reduce our shyness based upon these definitions?
I) The first part of shyness can be reduced by developing our awareness to a level where we are aware of the unconditional love within ourselves, can focus on it at will, and are fairly established on focusing on it/in our awareness of it as a default way of living. Once we are aware of this unconditional love within ourselves and are focusing on it, and moreover established on it, meaning that part of our attention is on this unconditional love more often than not, then we will have reached a level where we can see through judgments that say that we don’t deserve love, or that we can’t feel love because of this or that condition or situation when we are centered (on unconditional love). We can see through them when they come to us in our experience and feel unconditional love directly within ourselves. This means, judgments of people cease to affect our ability to feel love within ourselves, cease to be able to make us unhappy. Therefore, our shyness is naturally reduced in this aspect, because there will remain no reason to fear people’s judgments in terms of not being able to feel love/as a cause of our unhappiness once we learn to use our conscious power to feel love any time we want.
Step by step instructions to reach this level of awareness: (Approach these instructions with your heart first and foremost as your guidance. Learn from your own experience and work to find your inner guidance, their primary purpose is this, and the side effect will be the reduction in shyness.)
1- Learn Breath Awareness Meditation from these 2 articles:
2- Read about also the Spiritual Heart meditation from the articles in step 1.
3- Start practicing Breath Awareness Meditation 5 minutes a day, and increase to 20 minutes after you can do 5 minutes for a few days. Do your best to turn this into a continuous effort. Remember you are not just adding meditation to your life, you are cultivating meditativeness, as an increasing trend.
4- Meanwhile, you will be becoming aware of the state of Awareness as you practice Breath Awareness Meditation. Study the two articles again, and you will deepen your understanding along with your practice. You will be learning what Awareness is through first hand experience and also receiving conceptual information/guidance from a highly realized person.
5- When you are progressing in your meditation practice, check your intuition, and if it feels right, start practicing Spiritual Heart Meditation as well. This will begin to teach you how to feel the energy of Divine Love/Unconditional Love directly.
6- Study this article for thorough information about what this is all about. You can do this while you are getting into step 5. When you are meditating more or less regularly and working to increase your meditativeness, you are already progressing towards the goal. You will probably be desiring to fill the gaps in your conceptual knowledge to better guide yourself towards your goal. This article is a great guide for that:
Notes on these steps: These steps are not strictly do this or that. They are designed to propel you towards self knowledge, true self confidence, and conquering your shyness. Proceed with your free will, with open eyes. Trust your inner knowing first while you are proceeding. Tailor these steps according to your own needs. You can benefit from the Search function on to further increase your knowledge in any topics/questions that may further arise.
7- As you learn more about Spiritual Heart meditation, practice keeping some of your attention on the Spiritual Heart throughout the day, and simultaneously living as Awareness. This is a powerful way to conquer the judgments in our minds. We create the experience of Unconditional Love in our lives, and the judgments that we experience lose their power over us, we gain by first hand experience the knowledge that Love is always available, we are the Awareness that everything is happening inside, and we are also the energy of Love (as we are advancing more and more.), this reveals to us that these judgments are temporary realities/beliefs that we have believed in/gave our power to. This step is expanding the state of meditativeness (Breath or Spiritual Heart focus and living as Awareness) into every part of your life. This is teaching you to be the real YOU, teaching you to discover your true freedom. And simultaneously conquering the shyness of being judged by people.
II) The second part of shyness, which is fear of being harmed by people/fear of survival is conquered with the same 7 steps. But it requires more practice, and reaching deeper awareness levels where we find out through experience that we are not the body, and we find out that we are one with all life. I am working on this step as well. There are masters such as Ramana Maharshi that had reached this level. There are other people who have shown tremendous courage facing life threatening odds. Live in courage to conquer this aspect of shyness and I believe you can be a great inspiration for humanity and your life would be a great benefit to humanity. As we develop the trust for life through our sincere practice, our fear of survival and our fear of being harmed by people is progressively reduced as well.
Finally, please be aware that we are not suppressing or rejecting your shyness. The suggested path in this answer is a path to increase your understanding of it and wisdom of how to conquer it through experience. So when you are shy, be accepting of yourself. The steps above are designed also to teach this.