Thanks for that explanation. I've been doing some low-level programming lately, and I'm getting interested on running stuff bare-metal. Every previous description of multitasking I've seen has been very hand-wavy.

Yeah no problem. Multitasking isn't really complex - it's generally split into two categories: collaborative and preemptive. Collaborative multitasking is simply having user programs call a yield syscall which tells the kernel that it's ready to give up control of the CPU and it switches to the next task, but this is not very secure and is uncommon on newer systems. Alternately, preemptive scheduling generally has a timer which goes off regularly which automatically switches to the next task. Choosing the next task is the next part which the simplest one is round robin, where you literally just have a list of tasks and it always selects the next task and gives each task an equal amount of time. You also have SMP versions (that work for multiple cores) and also priority-based schedulers (which give certain tasks, such as system daemons, more processing time). Hopefully that extra info helped a bit!