The soft sign ь doesn't have a sound of its own, but (as its name suggests) it softens (or palatalises) the consonant which it follows.
Compare the И sound to the short i in words like a bit, a little. In Ukrainian, it is very similar but a little longer and deeper. Think about И as the sound between і and у. Say iii and try to switch to ууy ― you will get И somewhere in between.
The soft sign (Ь, ь) is a letter in the Cyrillic script that is used in various Slavic languages. In Old Church Slavonic, it represented a short or reduced front vowel. However, over time, the specific vowel sound it denoted was largely eliminated and merged with other vowel sounds.
Щ - is pronounced like two separate sounds: ШЧ. Consider the sounds the letters 'shch' make in these phrases: "Cash cheque", "fish chowder", "reddish cherry".
In Modern Russian, the letter "ъ" is called the hard sign (твёрдый знак / tvjordyj znak).
Zhe or Že (Ж ж; italics: Ж ж) is a letter of the Cyrillic script. It commonly represents the voiced retroflex sibilant /ʐ/ (listen). It is also often used with D (Д) to approximate the sound in English of the Latin letter J with a ДЖ combination. Zhe is romanized as ⟨zh⟩ or ⟨ž⟩.
Yu or Ju (Ю ю; italics: Ю ю) is a letter of the Cyrillic script used in East Slavic and Bulgarian alphabets. In English, Yu is commonly romanized as ⟨yu⟩ (or ⟨ju⟩). In turn, ⟨ю⟩ is used, where is available, in transcriptions of English letter ⟨u⟩ (in open syllables), and also of the ⟨ew⟩ digraph.
Compared to other Cyrillic alphabets, the modern Ukrainian alphabet is most similar to those of the other East Slavic languages: Belarusian, Russian, and Rusyn. It has retained the two early Cyrillic letters і (i) and izhe (и) to represent related sounds /i/ and /ɪ/ as well as the two historical forms e (е) and ye (є).
Today, both the Hard sign (Ъ) and the Soft sign (Ь) are used to separate a consonant and a vowel (mostly Я, Ё, Е, Ю), only the Hard sign (Ъ) separates a Hard consonant and a vowel, and the Soft sign (Ь) separates a Soft consonant and a vowel. In some other languages, a similar function is given to an apostrophe.
By the way, in Russian "ь" is called мягкий знак (myah-kij znak), which means "soft sign".
Ef or Fe (Ф ф; italics: Ф ф) is a Cyrillic letter, commonly representing the voiceless labiodental fricative /f/, like the pronunciation of ⟨f⟩ in "fill, flee, or fall". The Cyrillic letter Ef is romanized as ⟨f⟩.
Ge, ghe, or he (Г г; italics: Г г) is a letter of the Cyrillic script. It represents the voiced velar plosive /ɡ/, like ⟨g⟩ in "gift", or the voiced glottal fricative [ɦ], like ⟨h⟩ in "heft". It is generally romanized using the Latin letter g or h, depending on the source language.
Э э (Э э; italics: Э э; also known as backwards ye, from Russian е оборо́тное, ye oborótnoye, [ˈjɛ ɐbɐˈrotnəjə]) is a letter found in three Slavic languages: Russian, Belarusian, and West Polesian. It represents the vowels [e] and [ɛ], as the e in the word "editor".
The sound «Ш» [SH]
Like milk boils over or snake hisses. If the sound resembles whistle or you cannot produce it at all, do the following: stretch your lips, move the tip of your tongue to upper teeth and pronounce the sound «С» [S]. Pronounce it very slowly.
The Russian letter “ы” is probably the most difficult letter to pronounce. People say it sounds like the sound someone makes when being winded. This vowel sound should be pronounced like something between “i” and “u.” For the right pronunciation, try to say “u” with your lips open as if you're saying “i.”