One of the basic ways to look at the age of the Milky Way is to look at globular clusters. These are dense clusters of stars that are distributed in a kind of halo around our galaxy. We know that the stars within a globular cluster form around the same time, and we can determine their age by looking at things such as the percentage of their stars that are red dwarfs, or the temperatures of their white dwarfs.
The red dwarf measure is useful because red dwarfs can last for trillions of years, unlike larger stars which only last a few billion. So if a group of stars form at the same time, the larger stars will die off sooner, while the red dwarfs continue to shine. So the more red dwarfs a globular cluster has, the older it is. The white dwarf method relies on the fact a white dwarf is the remnant of a Sun-like star. Once a white dwarf forms, it has no way to produce new energy, so it gradually cools. The cooler the white dwarfs in a globular cluster, the older it is.
It turns out that the oldest of the globular clusters surrounding our galaxy are about 13 billion years old, which means the Milky Way must be at least that old.
Picture Credit : Google