Some people find talking in social situations much easier and can seemingly break into a group straight away, but that isn't always a good thing. Most social groups build up gradually and organically over time, and people don't instantly break into them as easily as you might think. When you see someone loudly and confidently breaking into a new social group, you don't know what they might say about them when they aren't around. It's much better to be invited into a social group than to forcibly break into it.
A group is of course composed of individuals. The key to being accepted as part of a group is to be accepted by the individuals that make up that group. They won't always be together. Rather than try to latch onto a group conversation, look for an individual to talk to. You don't have to force a conversation and tell them about yourself - take a genuine interest in them, and ask more questions than you make statements, even if that is just simply asking others how they are doing or asking them about their work.
'Social networking' is not something exclusive to the internet. The same principle applies in real-life situations. Just as adding one person to your social media gives you potential to branch out and interact with their friends, making a single friend in real-life is a bridge to new social groups.
In the work place, you could make it your goal to get to know everybody individually over time. Then, when everybody is in a group, you'll find it easier to speak because you know how each individual might respond or react. In social situations like parties, people will 'mingle' throughout the evening, becoming part of large group conversations for a while, but then breaking away for individual conversations. Go for the individual conversations, get to know individuals rather than try to break straight into the groups.
And don't be afraid of saying 'silly things'. Be yourself, and don't fake anything. I've seen it happen, especially in the workplace, where new people feel like they have to prove themselves by being what they think they are expected to be, and they always end up looking stupid. It pays to be honest and humble about what you know, especially at work. If you say you don't know something, you should get help and training; if you pretend you already know you'll likely end up making a mistake. The same is true in social situations - for example, if you pretend to like sports so you can break into a conversation about sports, sooner or later it will become apparent you know nothing about it and you've done yourself no favours. If you talk genuinely about your interests you are more likely to discover other like-minded people and form friendships.