This vowel does not have an equivalent in English. Try to invest some time in learning it and differentiating it from other sounds.
To get the Russian sound ы, you should place your tongue in the position right between the positions of English sounds i in kit and u in sugar.
*Note that this sound is different form the English i in bit.
Now practice these words:
дым быт был мыло мы
dim bit bil mi-lo mi
fog everyday life was soap we