The age of the universe is measured through a variety of methods, including the cosmic microwave background radiation, the ages of the oldest stars in our galaxy, and the observations of distant supernovae.
The cosmic microwave background radiation is the thermal radiation left over from the Big Bag, which can be measured to determine the age of the universe to be around 13.8 billion years old.
The ages of the oldest stars in our galaxy can be determined through radioactive dating of their composition, which gives an estimated age of about 13.5 billion years.
Observations of distant supernovae can also be used to measure the expansion rate of the universe, which can be used to determine its age.
These methods and others have been combined to produce a current estimate for the age of the universe, which is believed to be around 13.8 billion years old.