How is the age of the sun determined?
Sun is typically a Main Sequence star.
Sun is typically a main sequence star, typical lifetime of a main sequence star is about 10 - 11 Billion years as they burn fuel slowly as compared to Giant stars which burn fuel very fast and live for about a 100 million years.
The current life of a star is usually determined by the amount of fuel it has burned till now (Hydrogen to Helium). So, the current age of our Solar System, including our sun and other planets is roughly about 4.5 Billion years.
At 10 Billion years Sun would have burned all its hydrogen to helium and will transform itself into a Redgiant, in this state it'll burn Helium for another 100 million Years before collapsing on its core and becoming a white-dwarf.