I think of ь as adding a simultaneous 'y' or 'ee' asking to the consonant.
So в sounds like 'vuh' and вь sounds more like 'vee'. That isn't quite right, because they aren't two separate sounds, but i think it's close. Another comment linked to a comparison between кров (shelter) and кровь (blood); try listening for the little ghost of an 'ee' sound at the end of кровь and hopefully you'll hear it.
It palatalizes the preceding consonant. You can learn more about it here: https://en.wikipedia.org/wiki/Palatalization_(phonetics) Basically speaking, you have to move your tongue closer to the hard palate when pronouncing a palatalized consonant.