This is an answer for Unix. I'd lay good money on Windows being pretty similar as the solution has been around a long time and is well known to be robust. The details will vary a bit (different API calls, specifics of semantics, etc.)
It depends on whether the other end is using the pipe's file descriptor in blocking or non-blocking mode.
In blocking mode, the process is waiting in the OS kernel for the data to become available. The way in which notification happens there depends on the OS. Chances are it involves a queue of processes that are considered to be runnable, and everything's made simpler by the fact that the kernel can (largely) control what interrupts it. In a simple (single processor) implementation you could go for something as trivial as noting on write to the pipe that the other process is waiting to read from it (via some kind of “interest set”), and so marking the reader as runnable at that point (at which time it becomes up to the scheduler to decide).
In non-blocking mode, either the process is polling from time to time (yuck!) or they're using a system call like select() or poll() (there are some higher-performance variants too). That's very much like the Windows call WaitForMultipleObjects() and works just great with pipes. That in turn ends up back at that runnable process queue, the interest set, and the scheduler.
It also doesn't really matter too much whether it's blocking because the pipe is full or the pipe is empty, as the control flow is pretty much symmetric between readers and writers. (Unlike the data flow, of course.)