My elementary school burned down at one point - it was one of those "open classroom" schools with cardboard walls that could be opened up to make it all one giant room, so of course the cardboard walls burned out first and the roof collapsed. It was a bit of a problem as it was the only year-round-school in a county full of 9-month-schools, so it was actually off-schedule from the rest of the schools, in session when they weren't and out of session when they weren't, which helped maintain a sense of unity among the student population for the year they were scattered. (It also helped that our mascot was the dragon - hello, irony, school burning down?)
IIRC it was in October, pretty close to the beginning of the school year. They ended up dividing the student population among 3 of the nearest schools based on geography and busing. I believe each teacher was assigned a school; the admin staff was partially assigned to various schools but the ones like the principal rotated through and was checking on all the students/teachers.
Not sure what would happen to the sports teams. I would imagine that the fall team would be the most impacted, as all the winter and spring sports players could be told to try out for their host schools' teams. Most fall sports are played outside, so as long as the practice fields were undamaged they could bus the players over (or tell them to get their own transportation over) to the old school and still hold practices. Depending on how late into the fall season they were, they might just let any team that wasn't going to do well in districts or states just disband.
I'd imagine the student government would try to continue to function, especially if this is set in the modern day with all the scads of social media available to teens. In my day, we'd have been SOL, but today the student government could still try to organize homecoming parades and dances and proms - all held at places other than their school, like local hotels - via the internet.
On an epilogue-y note: The county rushed through the rebuild by grabbing the approved schematics from another local school to avoid all the planning part, and they started rebuilding as soon as they managed to clear away all the rubble. It was in the middle of an apartment community, so there was always someone around during the day and early evenings and they organized to provide food & snacks to the workers all day long so those guys decided they were going to put in 12 and 14-hour days to get the school rebuilt in something like 7 months, most of which was winter - it was pretty amazing.