How do we determine the isotopic atomic mass of U-235?

Depends on if you want to do it the math way or experimental way.
Mathematically, you can simply add the masses of each part of the atom. Uranium 235 is an isotope with 92 protons, 92 electrons, and 235-92 neutrons. Taking the masses of these particles together will give you the mass of the whole atom.
In this case, a proton is 1.672*10^-27 kg, an electron is 9.109*10^-31 kg, and a neutron is 1.674*10^-27 kg. This adds to 235.04 u.
Experimentally, you can run your isotope through a mass spectrometer to determine it's mass. These machines can ionize a sample, and using a magnetic field give the particles a certain energy. As the particle flies through the machine, heavier particles will land closer, like the difference in how far baseballs and bowling balls will go when struck by a bat. Using force equations, you can find the mass of your particle.
https://phet.colorado.edu/sims/html/isotopes-and-atomic-mass/latest/isotopes-and-atomic-mass_en.html