I'm a native English speaker. I'm having a lot of difficulty pronouncing the French "r" sound, which is a sound that I have never encountered in English. How do I learn to pronounce the French "r" sound?
What was most useful to me was to hear that the French 'r' was the voiced version of German 'ch' as in 'Bach' or 'Buch' (but not 'ich').
The reason is that, in my experience, the sound is much easier to pronounce as unvoiced than voiced. I think this has to do with the proximity of the location of the friction and the organ involved in voicing. Or basically, you do two things in a French 'r', friction and voicing. It is a voiced uvular fricative.
If so, separating the friction element for practice before adding the voicing may be what you want. The German 'ch' is just a convenient sample of friction as isolated. I am sure there are may video instructions on it.
I am not a native speaker of either language.
Part of my motivation for writing this up as an answer is so the other members can point out anything I may have got wrong about the French 'r'. Thanks.
P.S. Also I sometimes find it easier to pronounce, lying flat on my back looking at the ceiling. This would make sense as the uvula is a fleshy protuberance. Where it rests may affect the sound. You may want to try different body postures as the thing may not work the same way for everyone.
I would say: don't worry too much and don't exagerate the "frenchness" of your r. When you start learning you might feel that you have to practice the pronunciation of r a lot. But after a while of listening you realize that even francophones make their r sounds unnoticed sometimes.
Don't try to sound your r like Edith Piaf, that wouldn't sound neutral. Listen a lot and try to imitate what you hear, but don't stress the r too much. And above all, enjoy the process of learning the language :)
In addition to the above answers, keep in mind that French has various ways of realizing the rhotic phoneme /r/. According to Wikipedia, all but the ones being described here are "considered dialectal". Rémy's sentiment that the "rolled" r reflects a "country farmer" accent supports that analysis, too.
That doesn't mean, though, that they aren't in wide usage. Depending on where you're planning to speak French, the alveolar trill [r], for example, used in many parts of French Canada, may be acceptable or even normal -- and in my anecdotal experience tends to be easier for English speakers to approximate. (It's essentially what we think of as the Spanish or Italian /r/.) I've heard the Francophone chair of a prestigious Canadian university language department who split his education across continents alternate freely between [ʁ] and [r]... so if he's allowed to do it, you may not need to worry too much. :) Often, the biggest leap an English speaker is looking to make is not to pronounce the obviously English rhotic [ɹ].
If you are determined to go further and master [ʁ] in particular, I've found two of the suggestions made above useful with my French students: to try to get something like German [x] (Bach) and move a little backwards from there, or to practice the very familiar English [h], move the tongue a little up from there, and vibrate.
I am a french native speaker living in an English speaking country :-)
The main advice i can give with regards to pronouncing 'r' sounds is to not put the emphasis on that sound in the words you are speaking. It is easier said than done, but you can practice with words which have 'r' sounds at the end , e.g. 'verre, guitare' or mixed with another consonant , e.g. 'promenade'
In those words the 'r' sound should be soft, a slight scrape of your tongue against the top back of your mouth.
A common thing i have heard english speakers do when speaking french is to scrape their Rs too hard, in which case it sounds painful to anybody listening!
There is also no need to roll the 'r' , it will give you at best a very strong country farmer accent and at worst a completely non french sounding accent :-).
The most difficult words are those which start with an 'R' sound, because you have to make the R sound a bit louder, but it should be the same technique to make it sound 'authentic'
Hope this is helpful!