We measure distances in universe by the units of light year/s or parsec. Which means distance traveled by light in one year equals one light year. Thus the lights we receive from the distant stars or galaxies are coming from many light years away.
So how do we know the age of the light so that we determine the distance it has traveled to reach earth?
We actually measure the distance, and infer the age of the light from the distance. There are many answers on the site discussing how cosmological distances are measured.
You can misure the redshift $z$, from which $z=\frac{1}{a_e}$ you obtain the Scale Factor $a_e$ that the Universe had when that light was emitted. But the scale factor is directly related to the age of the universe, so you know the age that the universe had when the light was emitted.
