I suggest going to google translate, setting input language to Swedish and entering "Man. Män. Man. Män.", then click the little speaker icon and listen to the difference.
Worth noting about the letter ä is that when pronounced as a short vowel it sounds like a short e. For example the Swedish word for but - "men" - sounds exactly like the Swedish word for men - "män".
Usually the apostrophe precedes the stressed syllable. For instance in the English "men" we would write it ['mɛn] (except that there is only one syllable, so it’s useless to write that it’s stressed). So if you write the apostrophe before the n, it would mean that the [n] is a syllable on its own and is stressed. It looks a bit weird but it could be the case.
Is there a difference in pronunciation between "män" is Swedish and "men" in English?
Thanks! Yep, the apostrophe is before the stressed syllable (see on Wikipedia: http://en.wikipedia.org/wiki/International_Phonetic_Alphabet#Suprasegmentals or on a random word in any English dictionary, for instance http://www.oxfordlearnersdictionaries.com/definition/english/because ). Of course it may be the case that the stressed syllable begins with a vowel.