How does the School Board work with the Superintendent?

This is dictated by State law.  The school district's organizational chart has the Community on the top, because they elect the individual Trustees.  The Trustees AS A TEAM hire and oversee a Superintendent.  The Supe then hires and manages all the staff members.

The job of the Superintendent is to be the educational expert who makes recommendations to the board.  The job of the trustees is to bring the values of the community to the process, and to task the Supe with goals that reflect those values.  They are also responsible for evaluating the Superintendent's progress toward those goals.  (They have a few other duties like acting in a judicial capacity to hear grievances--I'll tackle those in another post.)

It can be hard for school board members to limit their involvement to an oversight role.  In my opinion, people with strong backgrounds in business find this easier than others; those with backgrounds in education find it harder than others.  It is like Mom and Dad telling Girl, "fix dinner".  That is a nice clear task, but if they then hover in the kitchen, fussing about what is going into the recipe and adding things to the pan while Girl isn't looking.  Now, factor into that equation that Girl went to Cordon Bleu and is a professional chef with many years experience.  Mom and Dad gave the professional a goal, but then didn't let her accomplish it.  It's not fair to evaluate Girl's recipe when Mom and Dad have messed with it, just like it isn't fair for the Board to evaluate the Supe's progress toward the goals they gave after they've meddled in the details.

Also, if a school board member tries to do the work of the Super or of the staff, the staff will be confused about who their boss really is.  Let's expand the example above:  the family has three children, and Mom and Dad put Girl in charge of fixing dinner.  She gets Siblings to help, and tells Sib1 to add the onions and Sib2 to stir the pot.  When Mom and Dad interfere and tell Sib1 to put in garlic, and tell Sib2 to set the table (leaving what's in the pot to burn), to whom should the Sibs listen?  Mom and Dad have undermined Girl's authority by fussing with the details, leading to confusion about responsibilities and authorities.

There's one more issue with Boards "messing in the weeds" of running the district.  If they are busy in the details, no one is setting the goals and doing the work the Board is SUPPOSED to be doing!  And in that case, the district will, at best, tread water.  It won't be able to go forward because there is no one spending time and effort envisioning the direction the district should be heading.