How are atomic masses determined? The atomic mass (ma) is the mass of 1 atom of an element.
Elements have isotopes.
Therefore, there must be an atomic mass (ma) associated with each isotope of an element.
How do we know the atomic masses of the isotopes of an element?
https://www.ciaaw.org/atomic-masses.htm

The link above shows atomic mass (ma) data. 
How was this data generated?

Also, I have come across the atomic mass constant (mu). It has a value of 1.6605402(10) x 10^-27. 
How do I obtain this value? i.e. How was this number derived?
Thank you.
The mass of a particular isotope is determined by mass spectrometry. Hopefully you know this technique. In order to obtain a high degree of precision, the beam must go through several mass spectrometers coupled in series, some of which are quadrupoles or octupoles. It would take hours to explain the developments of this technique.