Part of the problem here is determining why you are shy. Are you shy because you are naturally an introvert or are you shy because you have been emotionally or physically abused (Please don't answer that here, the answer is not anyone's business but yours) or possibly both.
If you are an introvert, then this is a good book to start with:
As an introvert myself, I find it easier to communicate in writing or one on one. I would prefer to cut my right arm off rather than attend a party. Over time, I have gotten used to attending and participating in meetings. Sometimes you have to participate and you can start by getting with others one on one before a meeting and getting them to help you out at getting your message across. They can help you build your argument by giving you practice at presenting it in a less stressful environment. Also knowing that there are others who agree with you and who will publicly support your idea can give you more confidence going in. You can also reward yourself for participating when you were nervous about it by giving yourself some of the private time you need.
Consider talking to your boss and telling him that you are shy and will be more likely to contribute in a meeting if asked a direct question. Whether this is a good idea depends a lot on how extroverted he is (many strong extroverts just don't understand the problem at all).
Consider suggesting workplace training on Meyers-Briggs personality testing. We did this at one place where I worked and it really changed the whole dynamic of the place. One thing we found out was about 90% of the people at the worker level in that organization (It was a profession where introverts were the norm) were introverts. About 90% of the managers were extroverts. We did an exercise where a group of introverts and a group of extroverts were given the same thing to discuss (the ideal weekend). It was absolutely stunning to see how each group handled group discussion. It was especially stunning for the extroverts. It really did make people more aware of how to deal with people of different personality types. For the introvert, learning how extroverts deal with the world is useful as you will have to deal ina world where they are the majority. You will see that things that you may consider rude (such as talking over people) is so normal to them that they don't even notice it. Knowing that most people won't take it badly might give you more courage to butt in yourself. It might also serve to help you not lose confidence when people do it to you.
It also helps a great deal to have decompression time after work. Introverts are energized by ideas and people sap their enegery. You still have to deal with people all day long at work, so make sure you have some decompress time at home every day where you can be quiet and alone. That will help fill up your energy well so that you are better able to handle dealing with people at work.
If the problem with shyness stems from abuse rather than personilty type, then please consider getting professinal help. A therapist who uses behavorial modification techniques is probably the best for helping you change your behaviors to those more useful in the workplace.