This is a weird one because it sounds good but is so often a big failure. People know this kind of character should be included, but they may go about it the wrong way and not actually write a strong female character. And then there's the problem of cultural expectations and ideas of what this really is, so even if you write a truly strong female character, there will be people in the audience who claim that what you've written isn't really one.
Here are some things that a strong female character isn't (necessarily -- she might be some of these things, but she doesn't have to be any of them):
- A warrior and expert in martial arts
- Stoic and emotionless
- Someone who punches a male character in the face as soon as she meets him
- Someone who doesn't do anything stereotypically feminine
- Someone who never has to be rescued or helped
You'd think from the way that "strong" women are so often written that a strong woman is Rambo in drag. On the other hand, there are people who'll complain that a woman isn't strong if she has any weakness whatsoever, if she ever needs help or shows emotion.
What is a strong female character? Really, it boils down to a person who makes decisions and takes action that affects the story.
This is where a lot of attempts at strong female characters fail. Some critics are calling it "Trinity Syndrome," after the character in The Matrix. These are characters with a lot of traits we think of as "strong" -- they're strong fighters who are tough and hard. They may say harsh things to the hero or even hit him. They seem to know their way around the situation and may even serve as a guide to the hero at first. And then they're abruptly sidelined for the rest of the story, playing the kinds of roles that women typically get in stories, where they either have to be rescued, prop up the hero, make the hero feel sad if something happens to them, or serve as a reward for his success.
If you could replace a female character with a valuable object without the plot changing significantly, you don't have a strong female character, no matter how many black belts she has. The hero might be seeking to obtain this object/person, he might be rewarded with it/her if he's successful in reaching his story goal, having this object/person makes him feel better so that he has the confidence to go after his goal, or losing this object/person makes him feel sad or want revenge on the person who took it/her.
This doesn't mean that you can't have male heroes or that women always have to play a key role. But don't delude yourself into thinking you've written a strong woman when you haven't.
What are some traits of a strong female (or male) character?
- Intelligence -- able to assess a situation and come up with or contribute to a plan, able to think on the fly and improvise when the plan doesn't work (even a sidekick can do this)
- Skills -- yeah, martial arts might fit in here, but linguistics, communication skills, mechanical aptitude, and even domestic arts fit in here. The person who can glean and scrounge up a meal on the road is going to be valuable to a questing party, and there's a difference between this being treated as a real skill that is appreciated and "you're the girl, so cook us something."
- Resilience -- the ability to bounce back physically and emotionally when things go wrong.
A non-strong female character might sit in a tower and wait to be rescued. A strong female character might still be a prisoner and might still need some degree of rescuing, but she might improvise weapons from items in her cell that come in handy during the escape. She might be observing the guards, their personalities, and their routines so she can help guide her rescuers on their way back out. She might get out of her cell on her own and meet her rescuers halfway. She might have signaled her location. She might have won over one of her guards. Or even if she has to be rescued without contributing to her own escape, she holds up to torture rather than giving up her side, and she observes enough while a prisoner to get valuable intelligence that helps her side. She does something that makes a difference in how the story goes.
One trap that's easy to fall into when attempting to write a strong female character is the "not like other girls" trope (you can look this up on TV Tropes if you have time to fall into a rabbit hole, but I won't link because I'm a nice person). That's where the character's merit isn't measured against an ideal or against the entire species, but rather just against other women. The message that sends is that women are useless and silly, but this one woman is different. I really hate it when I see this in children's and young adult books, and it's endemic there. This is what you get where all those other girls are silly and useless because they like girl stuff like clothes and boys and romance and cooking and sewing, etc., but this one girl is awesome because she's not like them at all. She's more like a boy and likes sports and fighting and action. This, to me, is worse than the damsel in distress because at least the damsel isn't being demonized for being female. She's considered desirable even if she's essentially an object. The "not like other girls" routine demonizes the entire gender in order to prop up one character.
Not every woman in a story has to be a strong character, but then again, neither does every man. There are sidekicks and human scenery. It's just more common for the female characters to fall into those roles, so it's good to take a look at the people you're writing.
Next, I'll tackle one that may seem to be odd as a problem character: the hero.