A good answer above, but from a grammarian point of view, there is more to it than that. In fact, it's very similar to the "less" vs "few" rule.
You use "many" when the item is a noun that can be counted. For example, "money" is not countable, so you cannot say "I have many moneys." (Of course you COULD, but that indicates many TYPES of money, and not "a lot" of dollars, for example. It would have to be money from other countries). This leads to my next point: you use "much" when the item is not countable. Seeing how you can't really say (without making much sense), "I have three monies," you use "I have much money."
Similar examples would be the use of the word "candy." "Candy" is a collective, or a countable, concrete noun. You can either say, "I have much candy," (to which you could reply with "how much candy do you have?") or you could say "I have many candies," (to which you could reply with "how many candies do you have?"). If the word is collective, which means that it contains a number intrinsically (per se, if you will), then you use "much." If the number can be counted (1, 2, 3, etc) then you use "many."