We use much with uncountable nouns and many with countable nouns. Note that much and many are mainly used in interrogative and negative sentences.
How many cousins do you have? (countable)
How much money did you spend? (uncountable)
Note that how much can also be used when we want to know the price of something. In this case, we can use how much with countable nouns (both singular and plural nouns).
How much does this dress cost?
Much and many can be used in affirmative sentences in combination with too and so. In this case, they denote the excessive amount of something.
I don’t know what to do with so much sugar!
There are too many people in here.
How .................... dresses do you have? - Not ....................!
There isn't .................... space for storage in my apartment.
-How many friends do you have?
-I don't have many friends, but I don't think that there is some standard to that.
-Yeah, I totally get it. Are you all in the same friend group?
-Yeah. We always have so much fun together even though that we don't have much free time now. We're all adults, have our own works, and duties, and responsibilities, so it's difficult to find time for hanging out.
-Well, many people don't have even that, so I'm happy for you.
Fill in the gaps with much, many.
Could you help me wash the dishes? There aren't .................... left.
I couldn't think of .................... good ideas.
How .................... dogs does your aunt have?
How .................... money should I have with me?
Why is there so .................... smoke in the kitchen?
How .................... electricity does this fridge use?
I hope, Mrs. Evans won't give us .................... homework today.
There were so .................... people on the bus that I decided to walk to the mall.
There are .................... rules to remember when you write an essay.
We don't see .................... swimmers in the sea in winter.