From: Piotr Gasiorowski
 
As has been determined on the basis of X-raying and cineradiography, there are two rather different articulations that produce virtually the same acoustic pattern perceived as "American R". Both are postalveolar approximants, but the active articulator (the tongue) behaves differently and takes a different shape in each case.
 
The retroflexed variant is made with the tongue tip raised towards the postalveolar area; the middle part of the tongue is lowered and almost flat. In the "bunched" version the body of the tongue assumes the shape of a ball; the tip is lowered and "tucked away" underneath, while the arched middle part rises towards the postalveolar/prevelar area of the roof of the mouth. In either case there is also some pharyngeal constriction (more for the buched variety) as the root of the tongue approximates the wall of the pharynx.
 
I'm not sure if these terms are easier, but I hope they are more precise than the forwarded description.
 
Many Americans use one of these varieties either predominantly or to the complete exclusion of the other, but it has been reported that some speakers can shift from the one to the other even within a single phonetic realisation of /r/. Reportedly, the variants are so similar acoustically that native speakers of American English cannot distinguish them by ear.
 
Piotr
Piotr sez:
"In either case there is also some pharyngeal constriction"
 
I think, in my case, there is a lot of 'pharyngeal constriction'. When I have described my Rs (I have at least two), I describe a constriction at the back of the throat to describe them -- almost a glottal stop; this is my first R. The other R is smooth, with no constriction at all. This last R is the one where the tongue is mostly at the bottom of the mouth, with the tip resting against the lower teeth.
 
But, as Piotr explains, there is the other R. When I exaggerate this R, this one can be curled back almost 360 degrees, where you try to put the tip of your tongue somplace way way back into the mouth of the throat. Well, more like someplace beyond 180 degrees, but the description suffices. And yes, there is a constriction in the throat. There is sum'n funny in my speech.
 
Curiously, to the satisfaction of my high-school-Spanish-teacher sister, I can do the pero/perro distinction in Spanish. One of them hits the alveolar ridge, the other one does not. I forget which spelling means 'but' and which means 'dog', but I can do the trilled one with a single clean alveolar tap.
 
Mark.