If you find an infant bird on the ground, don't immediately assume it needs rescuing. While you may not see any parents around they are very often watching closely from a safe distance and doing what they can to care for the young that has inadvertently left the nest.
A magpie chick who is without tail is most likely 1) still a nestling and would appreciate a fake nest made for them and stuck up a tree.
Fake nests can be made from an old ice cream (or similar) container, with a few holes put in the bottom to let the rain drain out. Put it up in the tree as high as you can and watch mum and dad come down to feed.
Chicks who have a tail and all the other associated feathers have fledged. They will look like adult birds, but young. They are called 'branchers' as they hop around on the branches practising flying and other life skills.
Magpies are unusual in that they spend a fortnight or so on the ground at this time. This is when they are often 'kidnapped' and bought into care.
For people with cats and dogs this stage of life can be very trying.