Today's CPUs are incredibly complex beasts. Sure, you can go rummage in computer architecture books and get a rough idea how a very simple CPU works. Understanding in detail how the CPU in your PC (or even your smartphone) works will require a lifetime, if not more. I suspect noone at Intel/AMD really undestands their latest CPU fully.
For example, today's processors take instructions from RAM, translate them into microinstructions internally, reorder and schedule those working even on several copies of the programmer-visible registers in parallel where possible (doing more or less the job of an optimizing compiler), and finally executing the resulting stream(s) of microinstructions.
Today's CPUs are much, much faster than RAM (in the time required to fetch a word from memory they can execute hundreds of instructions). Cache memory, and it's efficient use, predicting what will be read next, is crucial. Another area of significant complexity.
Add circuitry to compute the various operations, including floating point and assorted functions, like square roots and trigonometric functions. A box marked "floating point unit" right there.
And this doesn't yet consider the GPU that is integrated in some models...