SCF is needed to calculate the wave function of electrons in polyelectronic atoms since the wave function of one electron is dependent on wave function of another. SCF is viable for computing the wave functions of polyelectronic atoms, though it deviates from the actual functions a bit.
As for the actual calculation, SCF uses an iterative approach, where it first guesses/estimates the wave function of other electrons except for the first one, then a computer is used to solve the Schrodinger’s equation for the first electron by calculating the potential field for the first electron in every point in space (using the nuclear attraction and other electron’s repulsion calculated from average electron densities based on other wave functions). This yields the first iteration wave function for electron 1. The same process is repeated until other first-iteration wave functions are produced for the rest of the electrons. SCF will keep iterating until the modification in wave function from iteration to iteration plateaus.