"The King's Speech," which stars Colin Firth (the King) and Geoffrey Rush (his speech therapist), tells a story that shows how the king tried to deal with it (in the run up to his first war speech).
I liked the film, but found it painful to watch. As a teenager, people told me I had a stammer. I didn't, my brain just worked too fast, with the result that my mouth went at 900mph and got tangled up because it was expected to hustle a fair bit. Consequently, I had some idea what the king was going through (I don't think I'll ever forget how Peter Clements, Mathew Steiner, Daniel Plant or Larion Van Der Stalk took the mickey).
Incidentally, I'm told that some of the actors didn't realise that the Queen Mum was the wife of the King in this film. This makes me wonder; who did you think she was married to?