I have been recently reading a lot on the quantum mechanical theory regarding Density Functional Theory, DFT, and Time Dependent Density Functional Theory, TDDFT (Oscillatory and Rotatory Strengths in particular) in order to understand how first principle calculations fundamental theory work.

I get that DFT is used to calculate the ground-state configuration of a system and TDDFT gets you the excited states useful for spectra determination and that there have been developed several algorithms in order to make calculations more efficient (timewise).

But I still can't answer myself in a short way how does each one works (math aside).

If you were to explain them to a person that is not necessarily familiar with quantum mechanics, how would you do it?