This isn't a magic bullet, but when I want to make an effort not to seem arrogant (and I've been told that I sometimes come across that way) I start out by saying something like, "Here's what I think:" Then I say what I think. Then I ask something like, "What's your opinion on that?"
In theory, this lets the other person know that 1) I'm only voicing my own ideas, not claiming to have The Answer(TM) and 2) I value their ideas as well. It's worked okay for me, or at least, nobody has called me arrogant to my face lately. :-)
Also, I'd recommend that you do your best never to interrupt someone else while they're in the middle of a sentence. That's one of the best ways to seem arrogant that I can think of.