many / a few + [plural noun]
much / a little + [uncountable noun]
a lot of / lots of + [plural noun / uncountable noun]
These words say how much or how many, without a number. Which one you use depends on the noun: one you can count (books, people) or one you can't (time, money).
A lot of goes with both kinds of noun, in every kind of sentence. Lots of means the same and is a little more informal.
At the end of a sentence, with no noun after it, say a lot.
Many goes with plural nouns, and much with uncountable nouns. Both are common in negatives and questions.
In a positive sentence, use a lot of rather than much. After too, so and very, much is fine.
A few (with plural nouns) and a little (with uncountable nouns) mean a small number or a small amount, but some.
Without a, few and little mean "not many" or "not much", less than you want.