This is something I think about frequently.  The nature of cognition is elusive.  In order to be intellectually humble you need to recognize the many layers of bias, emotion, learned response and instinct that filter our views of the world around us.  We need to approach information with, first and foremost, a recognition of this accumulated bias.  We have to recognize the twinge of emotion that sends us intellectually in one direction or the other.  We have to be able to isolate ourselves from the responses of others before attempting to objectively view the problem.  We have to steel man the opposing supposition in order to find flaws in our own reason.  Above all else we have to place objective truth at the primacy of our aim and let that truth guide the arrow of pursuit as fletching to our accumulated knowledge.  And this is something we must do everyday to remain intellectually humble.