Re: How is the age of a star determined?

To determine the age of a star is a complicated process. We can not 
determine the age of a random star in space (except of the sun).  We can 
only determine the ages of stars if they occur in groups, called clusters 
by astronomers.  
Astronomers assume that all stars in a group (cluster) are formed at the 
same time.  But the stars in the cluster have different masses.  Now we 
know that the energy that a star emits (in all forms of light) is produced 
in the core of a star by nulcear reactions.  The most energy producing 
reaction is the fusion reaction that converts 4 hydrogen atom into 1 
helium atom.  4 hydrogen atoms have more mass than the 1 helium that is 
created.  The difference in mass (4x mass of H atom - 1x mass of He atom) 
is converted into energy (E=mc squared). Stars will produce energy by the 
fusion of hydrogen into helium for about 90% of their lifetime and lose a 
small fraction of their mass in the process.  
The lifetime of a star depends on its mass.  The more mass a star has, the 
hotter is its core and the faster the nuclear reactions will occur in its 
center.  The upshot of this is that the more massive a star is, the 
shorter is its lifetime, even though it has more mass available for the 
conversion of hydrogen into helium.  Think of this analogy: an RV has a 
much larger fueltank than a Volkswagen, but an RV uses about 1 gallon to 
drive 6 mi whereas a VW uses 1 gallon to drive about 30 mi.  Hence,  a VW 
with its 15 gallon tank can drive about 450 mi, whereas an RV with its 40 
gallon tank can only drive 320 mi. The same is true for stars.  Stars that 
have 15 times the mass of the sun, use up mass about 13,000 times faster 
and lives only about 1/1,000 times as long as the sun (about 10 million 
years as compared to the sun's lifetime of about 10 billion years).

How does that help us to determine the ages of stars?  Back to star 
clusters.  The more massive stars in the cluster will first run out of 
hydrogen in their cores (it has all been converted into helium). When that 
happens, the star will change its appearance and become a red (cool) 
supergiant or giant. Then the next massive stars will run out of hydrogen 
and change its apprearance and so on down the line. So we look at a 
cluster and see which stars are just beginning to change their appearance 
and determine the mass of these stars (that is another discussion).  
We can calculate how long it takes a star of a given mass to convert all 
its hygrogen into helium in their core. So from the mass of the stars that 
are just changing their appearance, we figure out the age of these stars.  
Since all the stars in the cluster have the same age, we then know the 
ages of all the stars in the cluster. 

Wow, this is a rather complicated way of getting to the answer.

The reason we can not determine the age of an individual star in space is 
that we can not know how much of its hygrogen has been converted into 
helium in its core (the change in composition in the core does not show on 
the surface of a star).  The only general statements we can make is that 
stars that are massive have to be young because they are using their fuel 
at a furious rate (the RVs of the galaxy).  That means that all red and 
blue supergiants have to be young because they are very massive.  On the 
other hand red dwarfs have little mass and they can be young or old 
depending on how much of their hydrogen has been converted into helium in 
their core and we can't know the answer to that.

I hope if I have not confused you too much and that this answers your 
questions.  It is very lengthy and I usually cover this material in about 
a week's lecture in college.

Reference: Any Introductory astronomy text book in the chapter on the 
evolution of stars.  For example,

Foundations of Astronomy, 4th ed, by M. Seeds,Ch 13, p 246 ff