Quick answer
Ы is an и said with the tongue pulled back, somewhere between “ee” and “uh”. Say “ee”, then pull your tongue back without moving your lips.
Ыы
Ыы
y
тыyou
How to say it
English has no equivalent. The nearest trick: say “roses” and hold the vowel in the second syllable, or smile while saying “oo”.
тыyou
мыwe
выyou (polite)
сынson
ры́баfish
мы́лоsoap
Why it matters
Мы (we) and ми́ло versus мы́ло (soap) differ only in this vowel. Get it wrong and the word still exists — it just means something else.
Where it never appears
Ы never starts a Russian word, and it never follows г, к, х, ж, ш, щ, ч — the spelling rule puts и there instead.
Typical mistakes
Saying ты like “tee”
tongue back: “ty”
Without the pull-back you are saying a different vowel — and often a different word.
жы, кы, гы
жи, ки, ги
Ы cannot follow those letters in writing.
Check yourself
Which word contains Ы?
ты — you.