Don't worry, everyone who has ever skated has fallen. They've fallen because they forgot to take their blade guards off. They've fallen by just shifting their weight while standing still. They've even fallen holding on to the rail. Don't forget to wear your bruises proudly.
Skaters consider bruises badges of honor.
The potentially most sinister type of injury is a concussion. Always try to tuck your head when falling so you don't hit it, but if you do and you either suffer a period of unconsciousness or are dizzy or disoriented after you get up, get off the ice and have someone drive you to a doctor. This is not something you should take lightly. Broken bones are always a hazard of falling, but can mostly be prevented by NOT putting your arms out to catch your falls. Of course, if it's a choice between your face and your arm and you must put your arm out, be sure and do it with a bent elbow.