How Does Evolution Work?

For the life of me I can't figure out how evolution works.  I mean, I know in theory how it works---mutations, what works is kept, what doesn't is discarded---but I can't figure out how it actually works. 

I've been reading a cellular biology textbook for awhile now, and I find myself asking the same question on every page.  At the subcellular level, life consists of sequences of chemical reactions between all manner of molecular structures, in highly regulated step-by-step processes, interdependent with and coordinated with other processes on the same or higher levels.  How does a strictly regulated, interdependent, coordinated, complex sequence of events evolve?  Does it evolve from another strictly regulated, interdependent, coordinated, complex sequence of events?  How does that happen?  If it's a necessary sequence---as it must be to be there in the first place---you can't just change it so that it does something else with no regulation or coordination; that would be disastrous.  It all has to fit... it all has to work... every step, every time, or else it's discarded - right?

I'm asking the question in all honesty.  Seriously, if anyone has an answer, please comment below.  I want to get specific though.  I want to get into the nuts and bolts of how some existing sequence evolved, every step of the way: what it was previously, what it was at every change and why that would be conserved, and what it is today.  I'm not interested in a 'Creation vs. Evolution' debate, nor will I respond to trolls.  If you don't have an actual answer then please just go away.