Q:

Do English language consonants soften?

Bonk's English course book states that they didn't at all. Where could someone obtain this necessary knowledge? Do you soften the first letter of DID rather than first of DO?

A:

"Softening" is a notion in understanding Russian pronunciation, and not applicable to other languages.  It generally involves raising the centre of the tongue during and after the consonant. The palatization of consonants in Russian is fairly predictable from the spelling.
In English there is no such simple rules.  In some dialects of English there is "allophonic" softening. That is the consonant is softened but it doesn't affect the meaning of the word. In American English, stop consonants are often slightly softened before /i/ American speakers are largely unaware of this, but it is part of the American accent. Listen to an American saying "cut" and "key", and you may note that the /k/ is softened in the second example.  However, an American speaker would not be aware of this, and cьut (to mix Cyrillic and Latin) would not be possible in a general American accent.  RP speakers in Britain don't soften like this.
At other times there is a clear palatisation: In "Cube" or the RP pronunciation of "new" the initial consonant is clearly palatised.
So softening does occur in some accents, but it is not used to distinguish different words, and most speakers are not aware of it.
There is another notion of "softening" in Enlish: some letters (c and g) have two very different pronunciations: cat or circle,  goal or giant.  This is also sometimes called softening, but is very different to Russian softening.

