I grew up in a family with no communication between each other and not liking each other very much. Now I am a shy person and need to get over it. I am an ambitious person too and I always have good ideas but have problems expressing them.
How can I overcome shyness? Be able to communicate freely without panic? To have self confidence and stop thinking of the negative things other people might think?
The first thing I'd like to say to you is, you are OK the way you are. There is a stereotype in society that we all ought to be outgoing, party animals, able to charm anyone with a smile. In fact, about half the population are like you and me: reserved people. THERE IS NOTHING WRONG WITH THAT. The world needs both extraverts and introverts. I could not be a writer if I could not function in solitude.
At the same time, it is good that you wish to break out of a negative family pattern and learn to be a better communicator. One GREAT thing you can do is to join Toastmasters. Look them up at http://www.toastmasters.org/. Toastmasters is designed precisely to help develop the skills you are looking for. It builds communication skills: both speaking and listening, it enhances self-confidence, and teaches people to treat each other positively and with courtesy.
But also you can learn any skill you like, without joining an organization, or attending a formal course. One of my mottos has always been:
IF SOMEONE ELSE CAN DO IT
I CAN LEARN IT.
How do you learn any other skill? You might buy 'how to' books on the subject, but that's a guide only. You can't learn to ride a bike from a book. You watch people who are good at the skill, and imitate them. You practice, make mistakes and think about what went wrong, and try again.
Social skills are no different.