If you see a wandering or lost pet or domesticated animal, catch it and take it to your local animal shelter. Animal shelters can usually pick up a caught stray animal in their area.
A sick, injured, or otherwise helpless wild animal must be helped. According to the Animal Welfare Act, anyone who comes across an injured animal is responsible for helping them.
Do not extend an injured animal's suffering. According to the Animal Welfare Act, if an animal is in such a state that keeping it alive is an apparent act of cruelty, it must be put down, or made sure it is put down by someone else.
You can catch an injured wild animal in order to transport it to a care facility. First you must make sure that the animal is really in need of help. An animal is not necessarily abandoned even if it might seem so. For example, the offspring of birds, rabbits, and deer may seem abandoned to us, when in reality the mother may have purposefully left them for hours to wait for their return. The mother is always the best carer for their offspring. Keeping wild animals at home is only permissable for the time it takes to give them the necessary care they need. It is not permissable to take an animal from the wild to raise it.
Injured animals may perceive you as a threat and attempt to defend themselves, so it important to exercise caution. Wear protective gloves and maintain proper hygiene when handling injured, sick, or dead animals.
More information on wild animals:
I found a chick! What do I do? (pdf) (In Finnish)