I cannot locate the rest of my Russian books, but I have a little traveler's guide from Berlitz, so I am correcting some of the phonetics. Please let me know if my choices are correct as the book I am using dates back to 1973.
I lost my IPA alternate keyboard when I got this new computer, but I have placed the IPA vowel chart at the bottom of this post.
Letter - Eng. - Pronunciation
A, a - - - a - - - (uh) cup (Note: unrounded open-mid back vowel = upside down v)
Б, б - - - b - - - (beh) bay
В, в - - - v - - - (veh) vine
Г, г - - - g - - - (geh) gather
Д, д - - - d - - - (deh) day
Е, е - - - ye - - - (yeh) yet
Ё, ё - - - yo - - - (yoh) yonder
Ж, ж - - zh - - - (zyeh) like the s in pleasure
З, з - - - z - - - (zheh) zoo
И, и - - - i - - - - (ee) see
Й, й - - - j - - - (ee krahtkoyeh) ("y" in "boy)
К, к - - - k - - - (kah) key
Л, л - - - l - - - (ehl) land
М, м - - - m - - - (ehm) my
Н, н - - - n - - - (ehn) not
О, о - - - o - - - (o) hot (unrounded open back vowel) = unstressed "ah"
П, п - - - p - - - (peh) pot
Р, р - - - r - - - (ehr) run
С, с - - - s - - - (ehs) see
Т, т - - - t - - - (teh) tall
У, у - - - u - - - (oo) book, boot
Ф, ф - - - f - - - (ehf) football
Х, х - - - kh - - - (khah) back consonant = Scottish "ch" as in loch, Bach.
Ц, ц - - - ts - - - (tseh) sits (nothing in English comes close, found in Greek and in Danish)
Ч, ч - - - ch - - - (chah) chair
Ш, ш - - - sh - - - (shah) shut, shoes
Щ, щ - - - shch - - (shchah) ??? - like sh followed by ch
Ъ, ъ - special symbol -- (tvyordiy znahk) - ** - indicates a compound word should be separated
Ы, ы - - - Y, y - - - (yehree) hit, bit, did - (lax close high front unrounded vowel; looks like a capital i on the IPA chart)
Ь, ь - special symbol -- (myahkee znahk) - * - softens the preceding consonant
Э, э - - - eh - - - (eh oborotnoyeh) met
Ю, ю - - - yu - - - (yoo) usually, duke
Я, я - - - ya - - - (yah) yard
- Ь, ь - "gives a 'soft" pronunciation to the preceding consonant. A similar effect can be produced by pronouncing y as in yet--but very, very short--after the consonant. In our transcription we shall show this with an apostrophe (') after the soft consonant." (reference: p. 10, Berlitz Russian for travelers, 1973.)
** Ъ, ъ "is sometimes used between two parts of a compound word, when the second part begins with я, ю, or е to show that the pronunciation of the word should incorporate a clear separation of the two parts." (reference: p. 10, Berlitz Russian for travelers, 1973.)

http://www.phon.ucl.ac.uk/home/wells/ip ... tm#display