Okay, well, the kind of club you describe is very rare in jr/sr high school. And anyone is free to start a club, but they may struggle to find members, facility, and a coach.
In jr/sr high, the closest to a club you can learn to play instruments is probably a brass band club. Now, as it is in most countries, a brass band club is very much like an athletic club in the sense that practice and discipline are required.
So every meeting tend to be practice, practice and more practice. If the school is facing a big event, such as a festival, competition or sports event, they become busy because they need to represent the whole school through the musical aspect. Then leaders need to discuss finances, equipment, events, members, etc., as someone previously pointed out.
In any club, however, it's not always the students who teach the newcomers. The ones who "teach" are usually coaches who are either hired from outside the school or are ordinary subject teachers helping out from his/her experiences. Students usually just give advise (which is influential too).
Back to the topic, since school starts in April, a meeting in May can be one of the first meetings in a club activity. In fact, freshmen usually can't enroll in clubs until perhaps May. So up until that, older members will be discussing how they can recruit the freshmen, how they can present their activities to the freshmen and so on.
Typically, a music club of any kind would gather at the music room of the school. Schools always have a music room, because music, including learning some kind of an instrument, is part of the compulsory education (or sort of, since sr high is not compulsory ed).
But some clubs don't get to have their own gathering room. In that case, they obtain the school's permission to do their activities elsewhere. But in reality this is quite rare, and clubs that don't get rooms just tend to fail being established in the first place.
Now, if this were in a university, it's a totally different story.
Like someone wrote, you should try to join a group of people doing an activity of the same theme, aiming for the same goals, even if it has to be on-line. You will see that in order to run such a group, you need to discuss certain future schedules in certain months. And sometimes you have to see members clashing between each other, or you'll see the joy of achieving something big as a group.