I would like to know how these two words differ in usage. Which one is singular? Which one is plural? I would greatly appreciate if you could provide me with a sample usage of these phrases.
Elizabeth Phrase in her book "English without tears" explains the difference between a little and little, saying they could even mean opposite things. She gives the following example:
The medicine he took did him a little good.
She explains that this means that the person actually had an improvement as a result of the medicine he took, in contrast to "the medicine he took did him little good" which would mean the medicine actually worsened his condition.
In most places where either one would be valid to use, "a little" has the connotation of being significant, while "little' implies an insignificant amount.
For instance, "I am bothered little by your statement" means that I may be bothered by some nonzero amount, but it is hardly worth my attention. By contrast, "I am bothered a little by your statement" implies that though I am only bothered a small amount, it is significant enough to warrant my attention, and hopefully yours.
Other uses generally call for one or the other. "little" as used as an adjective refers to physical size of one or more countable nouns: "A little man" refers to one single man who is little. The indefinite article "a" refers to this indefinite but countable "little man".
"a little" can also be used to signify quantity of an uncountable noun. "A little jam" is synonymous with "a little bit of jam" and turns the adjective, applied to the implied countable "bit" noun, into a quantifier for the uncountable noun "jam" (you don't refer to "jams" in the plural unless you are talking about jam made from different fruits, so you also don't specify a quantity of jam in terms of one, two, three, few, many; you specify quantity as a little, a lot, some, more, less, but not in definite units).
Both describe a small amount of, and the only difference, is difference of usage. For example:
Let's say there was a man with $25 in his pocket, and he was asked to buy sundaes. If he replied:
I have little money.
The natural 'next sentence' would be "I can't, I'm sorry". However, if he replied:
I have a little money.
The natural 'next sentence' could be "I might" or "Yes, I will."
"a little" has a 'negative' nuance, while "little" has a positive nuance.