The letter ы is the trickiest letter of the Russian alphabet, at least for the English speakers, as there is no such sound in English.
There are no words in Russian starting from the ы, therefore we don't display it in big caps. In transcriptions it is often shown as y.
Many beginners sometimes confuse ы with ь. Pay attention, the ы has a separately standing vertical line at the end which no other Russian letter has (and there is no l in the Russian alphabet).
Put your lips in the position for ee but start pronouncing oo. The resulting sound should remind you a sound that one would make being hit in the stomach.
Practice with syllables
Words with this letter
Practice with a worksheet
Practice the hand-written Russian letter Ы as well as the syllables and words listed above, with this worksheet: download the worksheet.