Pet Peeves: Number v. Amount

The word number seems to be disappearing and seems to be increasingly replaced--erroneously--with amount.
           Amount: quantities or entities that cannot be counted or divided up; use with abstractions
           Number: usually countable things--even if there are too many to really count!

This can be complicated since  it is possible to describe the same thing using either abstraction, which can't be counted
          There is a small amount of water in the glass.
or specific measurements, which can:
          There are 2 ounces of water in the glass. I can measure the number of ounces with this beaker.

uncountable: I have an enormous amount of grading to do.
countable: I have an enormous number of papers left to grade.

"Grading" in the first sentence is an abstract noun that cannot be broken down--it might include commenting, thinking, sorting papers, procrastinating, making decisions, and so on. It's a mental operation (at least for writing instructors who can't use scantrons).  While I can count the exact number of papers left to grade, the intellectual work of grading itself is indivisible. 

Ask yourself:  is it possible to count this, or break this into discrete, individual items?  If so, use "number."

A number of additional examples; a possibly unnecessary amount of advice.

Wrong: I have a large amount of friends.  Are all of your friends one, indivisible entity? They'd probably like to think that you consider them as individuals, therefore:  I have a large number of friends.

Ok, so maybe the number is so large that it seems abstract.
 The amount of people in the world is enormous. 
Still wrong.  I'm certainly not going to count them, but, theoretically, I could and they exist as individuals, so it really should be: There are an enormous number of people in the world.

A number of ideas; a small amount of knowledge?

And, if what you really want to know is the difference between affect and effect, here's the grammar girl.