Lilli Lehmann, the imperious dramatic soprano, wrote in her idiosyncratic book How to Sing that a singer without a trill was like a horse without a tail.

She also wrote that in practicing it, one had to almost scream. Scream? Lilli, for all her literary excesses, was of the 'you-must-have-more-than-you-need-so-that-you-have-what-you-need-when-you-need-it' school. After all,  she began her career as a coloratura soprano and ended up singing Isolde and Brunhilde, which must have taken a great deal of care and incessant work.  

Then there is Luisa Tetrazzini reportedly practiced for a decade in order to improve it. The Swedish Nightingale known as Jenny Lind wrote that Manuel Garcia made her practice the trill (shake) very slowly, which may have been intended to address her worn voice. Is this the reason why quite a few old singing manuals assert that the trill makes the voice supple and corrects defects?

The trill wasn't just for coloratura sopranos. Every voice, from soprano to bass, perfected it. Stronger voices often acquire it more easily than lighter ones. This may suggest that the action of the thyroarytenoid muscles in the vocal fold are a factor. One manual, Grammatica o siano Regole di ben cantara (c. 1817) by Anna Maria Pellegrini-Celoni (she of the axiom 'He who knows how to breath knows how to sing') even contains the admonition that both notes must "come from the chest and never with the throat." 

How to acquire it?  The old singers and teachers had a few key suggestions.

1) Practice the trill on a major third, then the minor third, major second, and finally, the minor second.  The trill must be obtained on the interval of a major third before proceeding further.

2) Practice the slow trill. What is the slow trill? It's the sound of an old Chevy station wagon trying to start up. In other words, the oscillation between the upper and lower note is done slowly, and then speed up when the distance between the notes has full integrity.

3) Hammer the top note. This is what puts the oscillation in motion, and helps keep the distance between the two notes intact- a very important point. If the distance between the two notes collapses, it's not a trill anymore, but something more akin to a gargle or a neigh.

4) Practice the trill with the mouth closed. This helps one acquire a feel for the oscillation of the larynx.  

5) Don't breath too deeply (the last two suggestions come from Pauline Viardot-Garcia's Exercise book An Hour of Study).  

5) Practice the trill on open vowels.