You can think of it as follows: when, say, N and YA meet or D and YA, they "blend" at border.
Do you notice how the middle section of your tongue is raised for "Y" in "year", "you", "boy"? Well, you raise it simultaneously with pronouncing N, so the whole consonants changes.
However, when there is an apostrophe, no blending occurs: first, you pronounce M as in мама, and then я.
I cannot tell from a simple description. But "softening" is definitely all about the position of your tongue.
I am not quite sure what to suggest (I do not speak Ukranian). Maybe you can compare the Ukranian м'ясо to the Russian мясо and try to hear the difference. Note that in standard Russian unstressed A and O are the same ("sort of A-like sound"). In Ukranian and in northern Russian dialects it is not the case: unstressed O's are clearly pronounced. Otherwise the comparison is a pretty good way to understand what's happening.
And, by the way, "softening" usually leaks into the following vowel, too (meaning that "A" in "дядько" is not quite as open as in "мама" because your tongue is still quite high; native speakers do not consider these deviations an impornant difference)
Shady_arc offered a good advice.
Listen мясо in Russian (http://forvo.com/word/%D0%BC%D1%8F%D1%81%D0%BE/#ru) and м'ясо in Ukrainian (http://forvo.com/word/%D0%BC%27%D1%8F%D1%81%D0%BE/#uk)
Do you mean the verb conjugations? http://wiki.verbix.com/Languages/Ukrainian
In English most people do not add the word all. "you" by itself is enough and is plural or singular. The original singular version "thou" is simply not used anymore and can only be found in old songs, prayers and literature. We use the plural form even for singular. We just face the person we are talking to and if there are other people in the room, name the person. "John, will you please close the door?"