I have tried like five times to fashion a response to this question, and all I can't think of is, the show will always dictate how you are going to tech it. You can't treat every lighting designer, every show, every tech the same, you need to approach it with an openness and flexibility to do what is required to get you from the first cue to the last one, safely, artistically, and sanely by the time your tech process is over.
So much of how you tech a show is about your own personal style - how one person works, is not going to be how another person works. And what works for me, may not work for anyone else.
By the time you sit down for the first day of tech, you should know what the problem areas are going to be (hard transition, quick changes, complex tech sequences), you should know how your lighting designer wants to work, you should have talked to your director about how they want you to run tech, you should know what your actors are going to need form the tech process, and you should know what the tech crew are going to need from the tech process.
To give hints or details, or share stories from my past, may just be confusing and wrong for another stage manager. For example, I rarely go back to for myself to call a complicated sequence, I wait for a director or designer to ask to go back. On my recent show, the LD was a couple of pages behind me most of the show, and I would just flip back and add the cues, and we worked on spacing and staging on stage. The first time I called the cues was during the first run. We held only for quick changes and staging issues. I have worked on shows where we dry teched EVERYTHING before an actor stepped onstage - so it was basically just walking them through and adjusting LX for blocking changes.
The act of running a tech is the defining moment in a stage manager's job - it's an extremely complex process, one that requires personal style and finesse and experience to pull off well. I know some really experienced stage managers who tech shows poorly. I think it's one of those things that time, experience and pondering techs past are the only way to improve. (If you ever have the chance, watch other people tech or have someone watch you tech - it's interesting observe stylistic issues without the pressure of being in the hot seat.)
So, I guess the way to start a tech is the way tech needs to be started.