In order to provide safety for all trampoline users, the proper safety features should always be installed on them, such as a metal frame covered with secure safety pads. To ensure safety on a trampoline in case of any falls, safety mats can also be bought and placed around the trampoline so that the fall would not be so hard. For even more security in ensuring that falls don't occur (or occur as often), purchasing a safety net accessory that's designed for the trampoline would also help, as it can be used to propel them off the trampoline.
With a netting around the trampoline, a child will be more likely to know where the edges of the trampoline are when jumping. This will not only help them avoid the edges but if they were to get to the netting, it would be less likely that they would fall off, as the net would be able to sort of guide them away.
For children who use trampolines as an enhancement to gymnastics, the trampoline should also have very thick padding on the inner edges of the trampoline. Since these thick padding aren't found very easily separate, the trampoline you purchase for gymnasium use should already include the thick padding on the sides of the trampoline. You can purchase padded end decks for the trampoline for better safety measures as well.
However, even with all the safety trampoline accessories, injuries are still bound to happen so it's a good idea to have supervision and "spotters" so that help won't be far if an accident was to happen.