I find that the softness/hardness of consonants is a lot easier with letters like "л" than with letters like "р". For instance, I find the word "мальчик" easy enough to pronounce, and it sounds very different to the л in "лампа". On the other hand, it's a lot more subtle to hear and difficult to pronounce the difference between the р in "ребёнок" and "рука" (although with practice, it can be done).

It can be helpful to think of pronouncing a tiny "y" (that's English y as in "yes", not Russian у as in "умный"!) sound after the soft consonants, but this should be voiceless, try to shape your mouth in that way without making the sound.

As for the letter "ы", I find this very difficult personally. It's basically the hard version of "и", so instead of imagining yourself making a "y" sound, imagine making an "ooh" sound, but again, try to make this silent. I've heard a lot of conflicting advice on how to pronounce this letter, but this is what I do, and I've been told by native Russian speakers that I'm pronouncing it right.

Some Russian sounds come more naturally than others to English speakers. With soft consonants and ы, I sometimes find that I have trouble, but practising the word over and over again (ideally with the help of a native Russian speaker) will help a lot.

Here are some resources that might help you:
  • LiveMocha - excellent website where you can hear voice recordings of words as you learn them, and also upload your own recordings of speaking exercises, to be reviewed by other members of the community. Also a good place to find people to talk to you using...[/*:m:1gyvt6fr]
  • Skype! - a great program for voice chat and instant messaging[/*:m:1gyvt6fr]
  • Wiktionary - has a good few Russian words with definitions, stress patterns, and often audio recordings too[/*:m:1gyvt6fr]
  • MasterRussian, the site you're on right now! Lots of the exercises and articles here have audio[/*:m:1gyvt6fr]
  • RussianLessons - some of the articles there also have audio[/*:m:1gyvt6fr]