Assume that the student (during his PhD) is faced with a problem which he and his advisor are both completely new to. The advisor is trying to help the student but owing to his lack of experience/knowledge/intuition in the field, is unable to help much. What is the etiquette for the student to seek external help (particularly professors who have dealt with such problems and maybe their grad students)?
Is it necessary to inform your advisor before going to other professors for help?
How should one introduce the subject of external help when the advisor is clearly interested in tackling the problem without any help?
You absolutely should inform your advisor that you are going to seek external help, even if they are against it. They are partly responsible for your studies and should know what's going on.
You could try introducing the subject as a collaboration rather than seeking help. If the person you want to approach has written a paper on the subject for example, you could say that it would be beneficial for your work to collaborate with them. As long as you at least create the impression that you're looking for interaction on the same level rather than just getting advice, I don't think you would have too much trouble convincing your advisor.