I �ve never really thought about it, here are some examples
I have a lot of money. - informal
I have much money. - Very formal and old fashioned.
I have a lot of things. - informal
I have many things. - formal
I don �t have a lot of money. - informal
I don �t have much money. - the same as I don �t have a lot of money
I don �t have many things - the same
I don �t have a lot of things - the same
I would say that for lower levels it�s enough just to tell them that "much" and "many" are a tiny bit more formal and that "a lot" doesn�t depend on whether it�s a countable or uncountable noun the way they do.
Anyone feel free to correct me here, I �ve never taught it so I don �t know the rules .