Use many with things you can count individually: 'How many emails did you get?' Use much with things you measure rather than count: 'How much time do we have?' If the noun has a plural at all — if you can count the things one by one — it takes many.
The core difference is countable vs uncountable
English divides nouns into two families. Countable nouns come in separate units and have plurals: one email, six emails. Uncountable nouns name substances, qualities or abstractions that you measure instead: water, time, advice, traffic. Many belongs to the first family; much to the second.
The test
Try putting a number in front of the noun. 'Three emails' works, so it is many emails. 'Three times' — no, not in the sense of duration — so it is much time.
A quicker version: does the noun have a plural at all? If yes, many. Chairs, reasons, mistakes, people. If it has no plural — information, luggage, progress, furniture — then much. Do not go by the letter -s: people is a plural without one, and news ends in -s but has no plural at all, so it takes much.
Nouns that trip people up
- Uncountable in English, countable in other languages: information, advice, furniture, luggage, news, research, equipment, evidence. All take much. 'How much research have you done?'
- Nouns that work both ways: 'much experience' (know-how) but 'many experiences' (individual events). 'Too much time' (duration) but 'many times' (occasions).
What careful writers actually do
Here is the part most guides leave out. In modern English, much sounds stiff in ordinary positive statements. Nobody says 'We have much work'; they say 'a lot of work' or 'plenty of work'. Much lives comfortably in three places:
- Questions: 'How much did it cost?'
- Negatives: 'There isn't much left.'
- After too, so, as, very: 'too much salt', 'so much noise'.
Many is freer and reads fine in positive statements — 'Many readers wrote in' — though it is somewhat formal, and 'a lot of' is the everyday alternative. This is register, not grammar: 'We have much work to do' is not wrong, just old-fashioned.
The safe middle ground
A lot of and lots of work with both countable and uncountable nouns, which is why they dominate speech. If you are stuck, they will not be wrong — but they are too casual for formal writing, where you should commit to many or much.
One more pairing worth learning alongside this: fewer goes with countable nouns and less with uncountable ones, following exactly the same logic.