Assertiveness is usually too simple a goal to be effective. Shy people typically go from resentful silence to nags or whiners in one step and then get frustrated when they meet resistance or get ignored.

The key is to speak up pretty close to when you first think you should. Holding back leads to coming on too strong and or over thinking of what you want to say. When you do speak say what you think one time, phrasing it as a question is good, and then leave it be.

Unfortunately being shy means feeling your under represented and ending up repeating yourself because it feels right. What gets missed is that every repetition weakens the message, causes resentment and makes you look weak.

People are creatures of habit so if people around you are used to your being passive your going to have to give them time to notice that what you say is worth listening to. Say something meaningful, make your point quickly and simply, and then let it go. Don't worry about being heard. Just practice speaking when you think of it in a natural manner.

Next time do the same thing. Wash, rinse, repeat. Over time people will notice. When they do you can then engage by asking a question. Don't overdo it. Don't repeat yourself needlessly. Don't whine. Slowly build credibility. It takes time for them to get used to listening to you and it takes time for you to calibrate what and how you want to communicate.

The other aspect seen with shy people is that often they are so worried about being heard and working on what they want to say they really don't listen. Possibly the first thing about communicating is having something to say. The easiest way to have something to say is to listen closely, ask questions, feed what people say back to them. Sounds silly but it works and can be the equivalent of conversational training wheels. People love it. It shows your paying attention. It also gets your foot in the door in a conversation.

Shy people have things to say. The problem is how to say it to people who are used to not listening to them without making it a drama. How to get heard without dominating the conversation or getting ignored.

It is an art. An art that nobody gets right all the time. Don't try for perfection. Make mistakes and laugh at yourself. Don't take yourself too seriously. Relax.