1) ''Yearn for'': it means ''to have a strong, often melancholy desire for someone or something''
E.g.: ''The sailors out at sea yearned for their families''.
E.g.: ''He sat alone in his room, yearning for his mother.''
2) ''Long for'': it is used to convey the same meaning of ''yearn for''. However, it holds the idea of a far greater desire, especially for something that is difficult or impossible to obtain.
E.g.: ''I long for the carefree days of my youth''.
E.g.: ''She longed for her old friends''.
E.g.: ''Unlikely though it may be, I long for the day when we shall regain our human rights.''
3) ''Crave (for)'': it also means ''to have a great desire for something''. However, it is rather focused upon something that you need urgently or that is related to one's appetite''.
E.g.: ''They craved for an unforgettable adventure.''
E.g.: ''There may be certain times of day when smokers crave a cigarette''.
Hope that helps!!! :)