I'd consider myself normal outgoing and I think, at least in a work environment, it is my self confidence that alows this. I know my input won't always be right, but it will be way more often than not- even then it will probably still have value. So I throw out my ideas in meetings where it's appropriate. I iterate on others ideas with them, that type of thing.

I would ask those around me what they thought of an approach- not because I was worried mine was wrong, because maybe they'd have a fresh take and could help tweak it for the better. This warms them up to collaborate. They will likely start doing the same to you, then you'll both come to a mutual respect for where each other's strengths and weaknesses may lie, but you've formed a bond of comraderie that should keep you well regarded. It's important that most of the time when you're asking for input that you've got the problem nearly licked- no one wants to work with the guy always asking how to do his job.

Those are the main ways I've built strong relationships in the office. I say hi to people as I pass buy, grab the odd coffee with whoever, and chat about sports (I happen to root for all of the rival teams up here, so that breeds a lot of conversation).

That's it- my secret is that I just behave like an okay guy most of the time and I don't stay silent and keep my eyes to the floor.