Trying to figure things out logically is necessarily dualistic.  There must be at least two things present in logic in order for one thing to follow another.

Trying to figure things out intuitively is necessarily singular because everything is considered at once, as one, without logic, discarding logic, and just *feeling it out*.

Logic is thinking.  Intuition is feeling. 

I believe that the only thing necessary to intuition is stopping the internal dialogue.

But that is often found hard to do.  In that case remember that you had to learn to talk.  The natural state of a babys mind is one of internal silence, and a barrage of external stimuli, enough to make it cry. 

So get back to the babys mind.  You dont have to stop the dialogue.  Silence is natural.  Just stop making the internal dialogue, a little bit at a time, ending the habit, and it will go away.  If you can do it for a second, you can do it for a minute.  If for a minute, then for an hour.  If for an hour, then indefinitely.