I thought of Lilli Lehman's teachings last night after finding myself on Youtube listening to a soprano well past her prime, the voice having lost its luster.

‘Lehmann herself avoided this fate, as evidenced in recordings made when she was in her 60's - some of which you can find here. Of course, she had quite a bit to say about keeping one's vocal youth in her idiosyncratic book How to Sing (1902), which you can find here.

I've excerpted a few passages below, taking the liberty of translating the notation of vowels into current IPA.

The head voice signifies, for all voices, from the deepest bass to the highest soprano, - leaving out of question the fact that it furnishes the overtones for each single tone of the whole vocal gamut, - youth. A voice without vibrancy is an old voice. The magic of youth, freshness, is given by the overtones that sound with  every tone. Height, youth, freshness of the voice = /e/ and /i/."  

So to utilize the head voice (resonance of the head cavities) that every tone shall be able to "carry" and shall remain high enough to reach higher tones easily, is a difficult art, without which, however, the singer cannot reckon upon the durability of his voice. Often employed unconsciously, it is lost through heedless, mistaken method, or ignorance; and it can hardly ever be regained, or if at all, only through the greatest sacrifice of time, trouble, and patience. 

The pure head voice (the third register) is on account of the thinness that it has by nature, the neglected step-child of almost all singers, male and female; its step-parents, in the worst significance of the word, are most singing teachers, male and female. It is produced by the complete lowering of the pillars of the fauces, while the softest point of the palate - behind the nose - is thrown up very high, seemingly almost into the head; in the highest position, still higher, thinking /i/ above the head. 

The back of the tongue stands high, but is formed into a furrow, in order that the mass of the tongue not be in the way, either in the throat of in the mouth. In the very highest falsetto and head tones the furrow is pretty well filled out, and then no more breath at all reaches the palatal and chest resonance. 

In the sensation of it, the larynx stands high and supple under the tongue- mine leans over to one side (see plates of larynx). All organs are elastic; nothing must be cramped or exaggerated. 

The vocal cords, which we cannot feel, now approach each other. The pupil should not read about them until he has learned to hear correctly. I do not intend to write a physiological work, but simply to attempt to make clear certain infallible vocal sensations of the singer; point out ways to cure evils, and show how to gain a correct understanding of that which we lack. 

Up to a certain pitch, with tenors as well as with sopranos, the head tones should be mixed with chest resonance. With tenors this will be a matter of course, though with them the chest tones are much abused; with sopranos, however, a judicious mixture may be recommended because more expression is required (since the influence of Wagner has become paramount in interpreting the meaning of a composition, especially the words) than in the brilliant fireworks of former times. The head voice, too, must not be regarded as a definite register of its own. If it is suddenly heard alone- I mean disconnected with chest or palatal resonance- after forcing the preceding tones of the higher middle range, it is of course noticeably thin and stands out to its disadvantage (like any sharply defined register) from the middle tones. In the formation of the voice no "register" should exist or be created; the voice must be made even throughout its entire range. I do not mean by this that I should sing neither with chest tones nor with head tones. On the contrary, the practiced artist should have at his command all manner of different means of expression, that he may be able to use his single tones, according to the expression required, with widely diverse qualities of resonance. This, too, must be cared for in his studies. But these studies, because they must fit each individual case, according to the genius or talent of the individual, can be imparted and directed only by a good teacher. 

The head voice, when its value is properly appreciated, is the most valuable possession of all singers, male and female. It should not be treated as a Cinderella, or as a lost resort, - as is often done too late, and so without results, because too much time is needed to regain it, when once lost, - but should be cherished and cultivated as a guardian angel and guide, like no other. Without its aid all voices lack brilliancy and carrying power; they are like a head without a brain. Only by constantly summoning it to the aid of all other registers is the singer able to keep his voice fresh and youthful. Only by a careful application of it do we gain that power of endurance which enables us to meet the most fatiguing demands. By it alone can we effect a complete equalization of the whole compass of all voice, and extend that compass. 

This is the great secret of those singers who keep their voices young till they reach an advanced age. Without it all voices which great exertions are demanded infallibly meet disaster. Therefore, the motto must be always, practice, and again, practice, to keep one's power uninjured; practice brings freshness to the voice, strengths the muscles, and is, for the singer, far more interesting than any musical composition. 

The passage above is filled with many hints regarding the acquisition of head voice, perhaps the most salient being the use of /e/ and /i/, which engender the aural sensation of vibration in the head. The reader should keep in mind, however, that these vowels are best apprehended when 'called' with Italian tonal values and absent any trace of diphthong.