Think of a wind or brass player rolling their tongue whilst exhaling into their instrument, IRF: that's how I understand it, but I'm sure an expert will be along soon to confirm or deny....

Here's an article that should help.

http://www.nuoboe.com/html/fluttertongue.html

Surprisingly, this is written in relation to the oboe, which conventional wisdom dictates is the wind instrument to/on which it is least suited/most difficult. Rolling "r's" is the way, but for those like myself who can't do that, an aggressive gargle is a reasonable alternative. Earliest use is probably in Strauss's Don Quixote, lots of it in music by the Second Viennese School but probably most effective in film suites by Hanns Eisler. And jazz, of course. Particularly effective on flute and mid-registers of brass instruments. Plenty of rather strange and unsuitable uses by composers in the 20th century -  one rather puzzling example by Igor in The rite of spring involves oboes and fast chromatic scales.

And the 21st (one tries one's best anyway)   

I'm thinking of works such as those featured on

http://www.amazon.com/Hanns-Eisler-Works-Orchestra-Vol/dp/B0000035V6/ref=pd_sim_m_3

Nos. 2 (Niemansland) + 3 (Kuhle Wampe) are probably the best known, or at least feature the best known Eisler material (the odd mass song). My memory of the fluttertonguing is probably exaggerated by the brass being muted much of the time.

The main two methods I know for clarinet correspond more or less to Italian/Spanish and French 'r's respectively (not the spoken version of the latter which I'm told is usually unvoiced and not much use for the purpose since it doesn't have any discernible repeated impulses, but a voiced version which sounds pretty weird if you use it while speaking... but if you sing rien de rien, je ne regrette rien with it, it sounds oddly familiar).

The former is probably more standard but the latter can be very nice as well - for me it's suited to quieter playing and the iterations are a little slower. Some composers ask for both of course.

There's a school of thought which suggests Stravinsky didn't know exactly what he was asking for in the flatterzunge markings in the Rite of Spring and actually wanted the staccato runs to sound like what they look like. I don't know chapter and verse for this one (or even if there's actually any chapter and verse to be found).

I have a feeling he might indeed have not known what he was asking for, since staccato and Flatterzunge are strange bedfellows at best (the saxophonist John Butcher can make a convincing combination of the two but this sound is hardly what Stravinsky would have had in mind I think), and at the speed of that passage hard to imagine at all. I suspect he was wanting rapid triple-tonguing in the staccato runs, and 32nd-note iterations in the second and third flutes.

A lapsed oboist writes:

Not at all impossible. Difficult, yes.