When to shift gears on a hybrid bike? I know what gears do what (what makes pedaling easier or harder), but my sister and I are having a debate on when exactly to shift. I think I read somewhere that it is better to shift when coasting or lightly pedaling and before the obstacle you are shifting to do better on. Sadly, I can't find the source so I have no proof to show her, she believes it doesn't matter when you shift it but it is better to do it while pedaling. Does anyone know which is correct?
It depends on your transmission. Some internal gear hubs, for example, are perfectly happy being shifted at a standstill.

For a derailleur based system, you should shift while in motion while pedaling lightly. It isn't ideal to shift under load, and shifts will be sloppier under load typically.

The question of when to shift while riding is a matter of personal preference -- ideally, you want to maintain your cadence or power output, but due to obstacles, you might downshift and get into an appropriate pedal position for continuing riding. It's like shifting in a car -- there are certainly wrong ways, but there isn't necessarily a right way. 

For example, if I need to round a corner and slow down before, I might shift down before the corner, get the pedals in a position I can round the corner without striking the pedals on the ground, go around and start pedaling again. But I could also get the pedals in position, slow down, come out the other side and downshift and continue going. Neither of these is wrong, but the first one is likely easier. 

It's also a good habit for coming to a stop and starting -- starting in a high gear is not so nice, and shifting down can be a bit jarring unless you build up a bit of speed in the high gear.