NASA/The Hubble Heritage Team (STScI/AURA)
From precise radioactive dating methods, the oldest things we can find in the solar system are primitive stony meteorites. They date to 4.6 billion years.
As they mature and use up their fuel supplies, stars change both their internal and external structures. Theory then suggests how old they are. Stellar vibrations, which allow astronomers to examine stellar interiors, work as well.