There are some grammar rules on the usage of "little" vs. "few", but since grammar is rarely the most helpful explanation, a good rule is that little describes the physical size of something, whereas few describes the quantity of something.
You could also think of it this way: That little is used to describe singular objects, and few is used to describe plural ones.
Here are some examples of few vs. little when used in a sentence:
"She has few hopes." vs. "She has little hope."
In the first example sentence, what is being described is the quantity of several things. (In this case, "hopes".) In the second sentence, what is being described is the amount of a single thing. The second sentence states that a single object, her hope, was small.
"An excellent author that few have heard of." vs. "An excellent yet little-known author."
The first example is a little tricker because what is actually being quantified is not directly stated in the sentence. Since we are talking about hearing of an author, the reader must infer that what is being described is actually the number of people who have heard of the author. Since "people" is plural, we use "few" to describe the quantity.
In the second sentence, what is being described is the size of the author's fame, renown or reputation. Since "fame" is singular, what we are actually saying is that the size of the author's fame is small.
Note that because both little and few have so many phrases they are used in which have evolved over time, the above rule isn't always applicable. Phrases like "In a little while," often get shortened to "In a little," in everyday speech, which is the same as "In a few." It isn't grammatically correct, but when has speaking ever been completely correct regarding grammar? :P
My apologies for the lengthy explanation. I hope this helps! :)