With the improvement of basic education and the increase of people's mobility, Mandarin has been spoken by more and more people in mainland China. Taiwan Chinese speak good Mandarin as well, in general.
I'd like to mention it that, in mainland China, affected by the phonology of their own Chinese dialects, people often do not speak madarin that well, though it does not usually makes trouble in understanding. Most people do not speak madarin as well as radio-broadcasters; and some even have trouble pronouncing some madarin sounds such as (in pinyin) r, zh, ch, sh, so as to replace them with similar sounds of their own dialects. For instance, [z](API, for s in rose, z in zero)/l for r, z for zh, c for ch, s for sh.
If you pronounce "ss"( for sh in shift) and "r" (r in red) very well --and I bet you do, then it's easy for you to do r in mandarin. You may shift the position of your tongue tip in some way or change the shape of your tongue ( especially the tongue edges, for example) and compare the sound that you make to the standard one. Keep doing this until you make your own perfect r.
For pronouncing r in mandarin, shift your tongue tip form where you make 's' or "ss" or 'r' to the lumpy part of the hard palate and point the tongue tip to it without touching, make a voiced consonant (or rather a semi-vowel) and you'll get the sound r in mandarin.
Adjust the position and shape of your tougue, and you'll heard a series of simillar and differnt sounds. Keep making the sounds, compare with the standard one until you make the perfect. Note that:
------ Your tongue tip is very near to the uneven part of the palate, but not so near that you can hear the puff sound, that is, r is not a fricative
------ The r in mandarin is a semi-vowel, and so its duration is very short and it always comes before a vowel; thus you do not extend it to a distinct length. (Actually you cannot lengthen it to such an extent as long as you've properly pronounced it).
I hope this ...