There is no really convincing way of determining the age of the Sun from observations of it. The way of determining the age is to measure the age of other solar system objects that we can get our hands on (i.e Earth rocks, Mars rocks, meteorites, the ``Genesis Rock'' from the Moon) and assume that all of us came together at the same time. More on this will be said in the solar system portion of the course. A large amount of astrogeological data indicates that the planets (and everything else) formed 4.55 billion years ago.
This means that the Sun is about halfway through its life. This raises the obvious question of what kind of afterlife the Sun will have.