Do you have a textbook with a audio CD?
1. Щ is something like SH in "sheet". English does not have a corresponding sound for Ш.

2. Russian uses two letters to represent the same sound, the Russian letters E and Э. The choice of which to use depends on several things, one of which is whether the previous consonant is palatalized or not. (The other vowel letters are similarly paired.)
English transcriptions are often based on certain transliteration systems, of which there are several in current use in the US.
Тhe sounds represented by letters E and O and Я depend on whether they are stressed or not. Unstressed E is often pronounced /i/- the same as И, unstressed O as /a/ same as A, and unstressed Я as /i/, same as И, but sometimes sounds like E.

3. You must memorize the position of stress in a word in order to know whether the letter O represents the /o/ sound or the /a/ sound. Stress position: compare English umBRELLa or inSURance versus southern dialect UMbrella, INsurance. I show stressed syllables as CAPs. In these English words there is no difference in meaning, but in Russian there are words spelled the same but with different stressed syllables and entirely different meanings. An example is the word ЗАМОК. Look it up in your dictionary and you will find two different words, depending on where the stress falls.

4. Г is usually pronounced /g/. There are some major exceptions such as foreign words, the adjectival desinence spelled -ого or -его, before voiceless consonants or on word end, where it is /k/, and a couple other rare instances. I don't know how to pronounce Гамлет without consulting a dictionary.

5. Ъ Ь Ы.
Ы is the vowel that is similar to И. It is slightly like the vowel in English "bill", "kick".
Ъ You will learn this in your second year or so. It has no sound but indicates how to pronounce the preceding letter.
Ь This also usually tells you how to pronounce the previous letter. It is called the "soft sign" because it indicates whether a consonant is palatalized ("soft") or not. It is also present with no significant meaning for pronunciation in some words that have kept their historical spellings. For example, the verb ending second person singular -ишь, -ешь.

Look in the learning thread here for recommended textbooks and buy yourself one. You definitely need one, because Russian is not a language you can learn by yourself, it is much harder than Spanish or German, for example.