Here are my tips about how to pronounce Russian sound Ы. Listen to the audio and repeat the exercises: 1) You go from sound "i" ("и") to the sound "ы". Start with pronouncing "i" ("и") long enough to get used to the position of your tongue and then move the tongue to the middle position in the mouth (move it a bit back from "i" ("и") sound position) and listen to the difference. Repeat the execrise few more times until you get the difference of the sounds. 2) You go from sound "u" ("у") to the sound "ы". Start with pronouncing "u" ("у") long enough to get used to the position of your tongue and lips. Here you need to change 2 things about your articulation. First, your lips move from round "u" ("у") position to the smiling, spread lips position of "ы" sound. Secondly, you move the tongue to the middle position in the mouth (move it a bit forward from "i" ("и") sound position) and listen to the difference. Repeat the execrise few more times until you get the difference of the sounds. Good luck!