Written explanations of a sound are inevitably doomed to failure, I think.
This blogger has a good stab at describing where your tongue goes to produce the r
My advice is to listen to a good sample recording of a native speaker and record yourself to hear what sounds you are producing. Practice. Practice some more.
(Worst case is if you don't quite master it you end up with a foreign accent, which you may well have anyhow. I doubt you'd produce a sound that will be confused with another mora.)
For just the kana sounds
AiueAoi is interesting and fun... although it's a little indistinct and in a childs voice
Wordchamp has a large body of sample words recorded. It also has a feature where you try to match a word's waveform. (This may or may not help you get a better pronunciation as I'm not sure it describes the aspect of the sound you need.)
I'm pretty sure jPod has lots of recordings of individual words and the kana, although some of this is in the premium area.