The scheduler is scheduled by
- an (external) event such as an interrupt, (disk done, mouse click, timer tick)
- or an internal event (such as the completion of a thread, the signalling by a thread that it needs to wait for something, or the signalling of a thread that it has released a resource, or a trap caused by a thread doing something illegal like division by zero)
In short, it is triggered by any event that might require that the set of tasks to be run and/or the priorities of those tasks to be reevaluated. The scheduler decides which task(s) run next, and passes control to the next task.
Typically, this "scheduling" of the scheduler is caused by the code associated with a hardware interrupt, or code associated with a system call.
While you can think of the scheduler as being a real thread, in practice it doesn't need to be implemented that way... because it is executed with higher priority than any other task. Sophisticated OSes may in fact set aside a special thread that is the scheduler, and mark it busy when the scheduler gets control. That makes it pretty, but the bogus thread isn't scheduled by the scheduler
One can have multiple schedulers: the highest priority one (e.g., the one we just described), and other schedulers which really are threads, and are run like other user tasks. Such lower priority schedulers tend to be used to manage actions which occur at much longer intervals, such as background jobs.