As a pedestrian, the first thing you should do to stay safe is to always obey the signals at a crosswalk. Do not try to dart across the road just because it looks clear. Wait for the walk signal, when you know you have the right of way and cars have been stopped at the light.
Of course, even doing this isn't perfect. One of the main reasons that pedestrians get hit is when drivers do not yield the right of way to them, even though they are in the crosswalk.
Now, there are cases where this means that a driver goes straight through on the same road that the person is attempting to cross. However, this also means the driver would have to run the red light.
Perhaps more common are situations where drivers turn through the crosswalk. They're allowed to turn left when opposing traffic clears. They can turn right on a red light or a green light.
Either way, the car leaves the road running parallel to the pedestrian and crosses through their path. The pedestrian, looking forward, may never see the car. The driver, watching the other traffic, may never see the pedestrian. All it takes is a momentary lapse for the two to collide, and the pedestrians always end up with far more severe injuries.
As you can see, there are plenty of risks, even when you use traffic signals correctly. If you get hit by a car and suffer serious injuries, it is imperative that you know all of the legal options you have to seek compensation.