School set-up guide (for teachers)
Setting up a cubing club is even easier for teachers! If you are a teacher then you already have a room and are presumeably allowed to use it for other purposes during lunchtime or after school. The school would love it if you were willing to run an after school cubing club and if you have enthusiastic and trustworthy students then you have very little to do besides let them use your room.
If you want to emphasise the mathematical elements of cubing then you are welcome to do so, cubing does have applications in group theory and other advanced mathematical concepts and many of the UKs top cubers are studying/have studied maths at university level. However, learning to solve a cube does not require maths and I would advise against focusing on the mathematical aspects too much as it can be off putting to students who don't really get on well with maths but are interested in cubing.
As a teacher, you have even more freedom to advertise the club to your students as they come to lessons, obviously you have to focus on what you are meant to be teaching in the lesson, but a short mention at the start or the end of the lesson is obviously fine.
I would recommend first ensuring you have some resources, you can get some basic cubes here and maybe some resources such as timers and mats, the sort of students who like cubes will also probably like to see their solve times so would love to have an official speedcubing timer to use at the club.
You can also help teach students to solve the cube, although in many cases they would prefer to learn themselves from other students or youtube, then you can come up with fun challenges involving the cube such as solving it one handed or handicap challenges based on the presumed speed of different students.