Learning soft consonants the "Carol Channing" way...
This is only partly в шутку ("in jest")!
Learning to distinctly pronounce the hard and soft variants Russian consonants can be difficult for foreigners -- especially English speakers.
But I might suggest that if you want to improve your soft consonants, you might look up "Carol Channing" on YouTube. Here she is performing the song "Diamonds are a Girl's Best Friend" (which was first made famous by Channing herself in the 1949 Broadway musical Gentlemen Prefer Blondes).
http://www.youtube.com/watch?v=7hZL4guaFKQ
Ms. Channing was not Russian, did not speak with a Russian accent, and as far as I know, she had no Russian background (she was born in Seattle). But for some reason, she always had a tendency to "over-soften" many of her consonant sounds. Not only does this make it easy for comedians to do a funny Carol Channing imitation, but it may also help you understand hard/soft consonant pronunciation a little better.
For example, most English speakers pronounce the first syllable of "diamonds" like дай- (with a relatively "hard" D), but Channing says it more like дяй- or дьяй-(with a very "soft" D). Also, listen to the way she says the "b" in "best", and the second "n" in "may be quite continental" -- again, rather close to a "soft" Russian б and н.
And her she parodies her famous role from "Hello Dolly", singing to a Muppet snake on "Sesame Street" -- listen to the way she says "so" at the 0:52 mark. The "s" is softened, and closer to сё than to со, in my opinion. (Между прочим, змею "Сэмми" озвучил Джим Хенсон.)
http://www.youtube.com/watch?v=0-UMlJhgQbY
Thus, you may be able to improve your pronunciation of soft consonants by adding just a little bit of a Carol Channing impression!
But don't overdo it and try to talk exactly like Carol Channing.
Because, (1) if you're a male, it will sound rather gay, and (2) to repeat, Channing didn't actually have a Russian accent, and (3) her vowel-pronunciations were also quite distinctive, and I'm only talking about her consonants.
However, her consonants often had a soft, Russian-like quality, as though she were putting a ь after them. So, watching some Carol Channing videos will NOT give you perfect Russian pronunciation, but it may help take you a step or two closer in the right direction, towards reducing your английский акцент.
