well now you're just getting into extremely basic microcontroller stuff. If you can't think of how to time some pulses, you really need to go spend some time learning to use whatever microcontroller you intend to use, because it's a very common and basic task.
However, have you actually tried this at all? Do you know the magnitude of the reflection you're going to see? Properly detecting such a reflection is still the harder part of the project. If you get a nice strong reflection from 10km away then it shouldn't be too bad, but if you're expecting reflections from tiny imperfections/damage in the fiber, which could be very low amplitude, you may still have a lot more of a problem. And if you actually need to measure these reflections in an analog manner, rather than just a digital indication of a reflection or not, you will have even more of a problem, because a simple 16MHz microcontroller won't be able to sample an analog signal nearly fast enough.