Here are the symbols I use for the Russian alphabet in the Russian
alphabetical order.
a b v g d je zh z i j k l m n o p r s t u f h c ch sh jh w y j e ju ja.
(a b v g d je zh z i y k l m n o p r s t u f kh ts ch sh shch - y ' e yu ya)
are the way most people transcribe them

I change the letters slightly so that there will be no ambiguity between which
letters are being used.

1. je after consonants I delete the j. b+je+z=bez (without)
2. ju, ja after consants I changed the -j to -i. m+ja+g+k+i+j=miagkij (soft)
3. e after consonants, I put between a -w- between them (it does rarely
happen, especially in English names: S+e+m= Swem (Sam)
5. a, u after i, I put a w between them: i+n+i+c+i+a+l+y=iniciwaly (inicials)
4. h after z, j, k, s and c, I put a k between the letters to distinguish them
from zh, ch, sh, jh, kh: s+h+i+z+m+a=skhizma (schism)
5. jh before i and not after a consonant, I drop the h: jh+i=ji (shchi,
cabbage soup).

This transcription, to my knowledge, works with all properly spelled Russian
words, even when transcribing words from non-Russian languages.

Vowels (glasnyje bukvy): a-je-i-o-u-y-e-ja-ju (note, jė is just je with two
dots over it, they are the same letter)
Consonants (soglasnyje bukvy): b-v-g-d-zh-z-k-l-m-n-p-s-r-t--f-h-ch-sh-jh
Semivowel: (first) j (kratkoje i)
Signs (znaky): w (hard one -tvėrdyj) -(second)j (soft one - miagkij)