Disclaimer: I'm surrounded by doctors and medical books, but have no official schooling in the subject myself. The medical knowledge discussed below is the result of personal research with the attempt to improve fiction writing, not to cure and/or diagnosis people.
Let’s say, for some reason, your character is babysitting and the child decides to cut the cord to a lamp with scissors. Why? Who knows, kids do funky stuff and apparently your character failed the babysitting class. But you do know the kid’s most likely been electrocuted. As would be someone doing any type of electrical work without turning the power off before hand.
If the current is low, it can cause a muscle spams preventing your injury-ee from letting go and stop getting electrocuted. Burns are also common where the current enters and leaves the body. Take extra care with kids, the current could stop their heart and lungs.
Obviously, the first step of treatment is to get the person away from the source of electricity. Don’t have your character touch them directly! If the kid is still in contact with a live current, your character runs the risk of also having current run through their bodies.
High voltage current, such are electricity in power lines and overhead cables, is dangerous. It’s usually fatal for kids and can ever throw a child some distance from the point of contact. Adults can handle more current, but high voltage is dangerous for everyone and will leave entry and exit burns. The most likely place to encounter such a current is from a downed line, so if your characters are out and about after a storm or the Apocalypse, this is an added element of danger.
Electrical burns are treated the same as normal burns, so nothing too special there. Cold water, cover it. My grandma is rather fond of using toothpaste on her burns, something about it being soothing.
I rarely see any type of electrical injuries in fiction, probably because for many people staying away from outlets and downed lines is common sense. But there are ditzy characters who lack that...and children who have yet to learn....
I'm going to pass on asking for real life addendums, because I really hope none of you have any. Aside from rubbing your feet on the carpet and then touching the doorknob of course.