Another trick: pronounce [u:] (like in boo) and smile wide when pronouncing. When pronouncing [u:], your tongue is in right position. All you need to change is your lips. Stretch them widely in a smile - and you'll get your pure Ы. It worked for all my students.

La letra rusa Ы http://www.youtube.com/watch?v=OK5bwA-XSfI

1. Just write this letter or some word with "ы" (мыло, мы) in google translate. There you can hear how to pronounce it. There is a button with sign (to hear). 2. Other way.=) You can smiling and repeat english letter "E"="И", still smiling you need to move your tongue slowly deep into your mouth and continue saying "И" , then "И" becomes "Ы". lol, I hope it helps you)

http://www.youtube.com/watch?v=qbkJGoL5tdE

http://www.study-languages-online.com/russian-articulation.html