Each utility generally has its own black-start procedures. One utility might start two diesel generators (only really used for black-start) and then slowly start energizing the path to various loads and other generators. That utility and it's parent RTO/ISO train on that scenario several times a year and have the procedure printed in a binder within reach.

Something I've found interesting is that many of these plans are ~35 years old and we're created before computers were super common place for these kinds of things. The point being people weren't doing graph and optimization algorithms to determine the optimal paths. There has been a little university research and national lab research into this recently and I've heard they've helped certain utilities that they worked with determine some improvements, which is always exciting.

The transmission level engineers and operators will call the shots as far as how the high level stuff goes down. In other words they'll issue a directive to get unit x online and then close in breaker b and clear a path to unit y while picking up load at z. The actual process from the end of the people doing that work is likely to be significantly more detailed.