How to use "a/an"

One of the most frequently asked questions is about how to use a/an/the. I've previously written two posts about "the," so today I'm going to focus on "a/an"

Meriam-Webster's Collegiate Dictionary (10th edition) says the following about "a/an":

• used as a function word before singular nouns when the referent is unspecified e.g. a man overboard
• before number collectives and some numbers e.g. a dozen
• the same e.g. swords all of a length
• used as a function word before a singular noun followed by a restrictive modifier e.g. a man who was here yesterday
• any e.g. a man who is sick can't work
• used as a function word before a mass noun to denote a particular type or instance e.g. a bronze made in ancient times
• used as a function word with nouns to form adverbial phrases of quantity, amount, or degree e.g. I felt a little tired
  

If this is too much to remember, the rule about "a/an" at a very very very basic level is that you need "a" before a singular countable noun or when you are defining/identifying something for the first time. For instance:

• But conditions have since deteriorated: the talks stopped in 2009, and that same year the United Nations imposed sanctions on Pyongyang after it conducted a second nuclear test and launched a long-range missile. North Korea also prohibited reunions between North and South Korean families (New York Times, September 16, 2010): Here, Jimmy Carter didn't say "the" second nuclear test, because this is the first time in the article he is referring to the test, i.e. he is talking about an unspecified event.
  
  

Make sense? :)