In most cases, the opening of schools went very much like the closing of schools at the height of the pandemic: city by city. As an example, at the same time in November 1918 while the Anne Arundel County (Annapolis, Maryland) County Health Advisor was announcing that schools were going to open, a group of teachers in Pennsylvania was refusing to go to work as some of their colleagues had gone to a conference and contracted the flu. Bascially, there was a constant wave of schools closing and opening across the country until June 1919 or so. By August and September 1919, Spanish Flu had pretty much burned itself out and schools opened normally.

That said, there was another major part related to the re-opening of schools. From a previous response on the Spanish Flu and schools:

One final note about the impact of outbreaks on school children. To us in the modern era, it can be overwhelming to look at the statistics around the Spanish Flu (195,000 American deaths in just October 1918) and have difficulty connecting to the human impact. While looking for articles about schools' responses to the Spanish Flu, I came across dozens of funeral notices in local papers for children who died, even some from families that lost multiple children in one week or day. School can sometimes feel like an impersonal space but those notices serve as a reminder that the adults working in them have long tried to do what they feel is best for the children they're responsible for, making the best decisions they can with the information they have.

School, especially in smaller communities, were faced with dealing with the impact of students' who had passed. In some cases, school leaders advocated for whole-school assemblies that served as a form of public mourning and flying the school flag at half-mast. Other school leaders, and teachers, advocated for a chin up, no acknowledgment approach that meant no discussion of students - or teachers - who had passed. So while schools then were different, they were very similar to today's schools in that the adults around the children were doing their best to keep the children in their charge safe, healthy, and learning.