At the end, the credits imply that Lionel Logue helped him with every speech.
The implication that the King was in a race to learn to speak well enough to guide his country through WWII is a dramatization, a taking of license with the facts.
My comments are not an attack on the movie as a movie (I have heard nothing but praise of it as a movie), it is just to point out that the movie is not completely true to the historical record. Sometimes movie makers move facts around a bit, like they were furniture, to improve the story they are telling.