There are 10 vowels in the Russian language. They can be divided into two groups (normal and soft ones) or 5 pairs where one of the vowels is a soft version of its counterpart.
Listen to these pairs:
As you can see, to make the second vowel in a pair, all you need to do is to add y in front the the first vowel (except for the last pair Ы – И).
The letter Ы does not have a corresponding sound in English and is indicated in the transcriptions by [ y ].
When a soft vowel follows a consonant, it makes this consonant soft (read about hard and soft Russian consonants).