If you read last week's tip on when to use less and when to use fewer, you are ahead of the game because the same principle applies to using the words number and amount. We use number for things that we can count or quantify and we use amount for things that we can't. Here are examples:
Number –- iPhones, paintings, glasses. There were a number of empty glasses on the table.
Amount –- food in the pantry, sleep, homework. What is the amount of caffeine in coffee? We bought a large amount of beer for the party. Now, technically, we could count those beers one by one, but the word amount refers to the sum total: the gestalt.