It's not very easy to picture something or someone not in existence and give them a certain level of three-dimensionality. This is true for virtually anything we write, but when it comes to speaking-characters, it's even harder.

Since I started writing professionally, it became increasingly more important for me to give "life" to characters that would be believable. Whether they are the heroes of a sci-fi action story, or the tertiary background extras of a romantic comedy, or part of a slice-of-life commentary, they have to feel real.

So, how do I write female fictional characters who are believable?

Well, when you start writing, you naturally gravitate towards something you're familiar with. Ever since we are kids, our make-believe worlds and adventures are filled with an infinity of "us." What we are, what we wish we could be, doing what we want to do or dream we could. Because of this, those of us who choose to pursue writing, will find it easier to write a character with whom we can more easily relate.

And I know some of you may be thinking: "Here we go. Another cis-gender know-it-all dude who is about to mansplain what a woman should be like as a character."
I actually understand why some may feel like that.

It's hard to relate to something created by people who don't understand it. That's why it makes sense to me that when a movie talks about the struggles of a certain community, or group in a society, most of the people involved in the production of the movie should belong to that community or group.

This brings me to my first step: understand and try to replicate. A writer is not necessarily alone. I wrote a whole other entry about it. I won't bore you with it, but you can find it HERE.
As individuals we are bound to certain experiences, life, past, hopes, dreams, views... That does not mean that we need to be limited by them. We can talk, ask people, research, and read. We can dive into knowledge that we cannot acquire through experience, but by learning it through what people share.

In other words, I, as an individual, cannot stop being a cis-gender man, but as a writer, that does not limit me. As writers we walk in other people's shoes, we try to understand and picture what our life would be if we were the character we are writing. What would we be thinking, what would we be afraid of? Would this character, given their background, talk like this or like that? Would they know what I know? What level of education have they achieved? What experiences have shaped them the most?

All of this does not necessarily need to be translated into words on paper when describing the character, but it can help you as the writer to move the character in a way that aligns with her story.

Avoid tropes. Tropes exist for a reason. Some might say that a trope or a cliché are such because they are classics. Well, I would argue that not all classics need to be perpetrated.

We are seeing more and more strong women in movies, books, comics, etc. Often, though, they fall into one of very few boxes that seem to shape most of these characters.
For example you have the godly, impossibly powerful super woman (very much like their male-trope counterparts).
Or maybe the genius who just has a talent for things.
Or maybe is the single mother who manages to keep her family happy through great sacrifice.

All of these represent strong women, but in most cases that is where the writing ends. The result is unidimensional characters to whom the reader or the viewer cannot easily relate. They don't make for bad characters, or for a boring story. They can be part of something very entertaining, but they are not realistic.

Add flaws and layers. So how do you create a multifaceted female character? Well you add layers. After all, not one person's life has one focus. We are torn among dozens of pursuits at any given time. Some aspects of a character's background may not serve the story per se, but they add realism and allow further immersion. The heroine who is all-powerful has dreams and hopes, memories that haunt her of bring a smile to her lips. Maybe she has a speech impediment, or a particular phobia. 
When you write her dialogue, don't have her ALWAYS talk about something that brings the story forward. It's a good practice to create dialogues that sound realistic; something that turns that moment of the story into a deeper connection between the character and the reader.

Anton Chekhov, a Russian writer, became known, among other things, for a theory that came to be referred to as Chechov's Rifle.
This dramatic principle argues that if an element exist in a story, then it must serve a purpose; it should otherwise be eliminated. 

If, at one point of the story, we see a rifle on the wall, then that rifle needs to be used by the end of the story or it has no reason to exist.

I tend to agree, but I interpret his theory differently. Very much like Hemingway said, we, as readers, tend to look for symbolism. I truly believe that most theories that are being written about different forms of storytelling were not even considered by the authors. 
Nevertheless, not everything needs to be tied to symbolism or potentially interpreted as such. 
The rifle in our example could serve several purposes. It's not only a prop. It could give us insight on a character. Maybe our heroine is a hunter; or maybe we could add more description to the room and see that there is a loaded rifle on the wall. On a small shelf by a warm fireplace, the light of the crackling flame reflects on a picture framed in a glass stained by age. Our heroine, as a kid, stands next to a dead antelope. She is in tears, while her grandfather towers over the trophy with a wide smile and proud look on his face, holding that very rifle. 

The description could go on to reveal more details, books, diaries, memories lost in the dust... that rifle will never appear again in the story, it will never go off, but it has guided the reader into more deeply knowing our heroine. We now see her not only as a crime-fighting badass, but also as a true individual; someone with a past and story, with memories.
She no longer is only that shell that were were introduced to, but has a soul.

This kind of tool can be used a number of times in a story, taking almost no time to read, very few pages out of the actual storyline, while creating a powerful bond between reality and fiction (in turn pulling the reader stuck in reality into the fictional world - thank you Neverending Story).

Even with this in place, though, we don't know of anything else our character is interested it. Ok, we know she is a videogame prodigy. We know that pixels and 1s and 0s speak to her as though they are part of her very being, but what is it that makes click other than that? A particular food? Does she have a crush maybe? Is she in love with another girl but is afraid to come out?
In the movie Rainman, the character played by Dustin Hoffman refers to a memory he has of driving in the driveway. We know of food he hates and food he loves. We know how he feels about kissing a woman.

All those scenes, tell more about him, but don't really move the story ahead. Yet, the movie would not be nearly as good, had those scenes not be introduced. We care for him, we care for his brother. We follow them in their journey, not only because we want to know how the story ends; we want to know what happens to them.

By adding layers to your character, she will not only be more interesting to write, but more likeable. Likeable does not mean that people will like the character or how she behaves. It means they will feel something.

All of this applies to any character you create. whether she is supposed to be liked or hated, a paragon of justice, or evil incarnate. "Liking" a character does not mean liking her personality or her actions. It means that she is so three-dimensional that she triggers emotional responses from the reader.

Avoid serving an agenda. We live in a world where all over social media we are exposed to people talking about men and women from every aspect. You have misogynists, androgynists, feminists, extremists, and so on. We all stand somewhere in these arguments.
We might want to create a fictional woman who fights for equality and rights for all women. Up until here we are doing a good job. Often though, writers go overboard by having a character speak as though she speaks for the author.

When we create a realistic fictional character, we can make her become the voice through which we express ourselves, our thoughts, our fears... but if that is ALL she talks about, if she pushes the agenda every time she can, it will feel forced. It will feel that she exists exclusively to push those thoughts rather than help the reader understand them.
As we write her, we need to understand we are not writing a manifesto, but a strong character who exists in a world. She is not single-minded: that negates openness and vulnerability. She is not always right: that negates growth and arc. She is not always pleasant/abrasive: that negates humanity. More importantly: she is not you.

One of the greatest obstacles I remember trying to overcome (I still am to a certain extent) was creating characters that did not have too much of me in them. Every creation has a little bit of the creator in it, of course, but we still need to be able to mold characters into something that we may not have much to do with. This is how we create realistic criminals; believable heroes; relatable fantastic beasts like dragons.

Get out of your own head. This is for all the men writing women (and women writing men could take a note too).
Fellas, do not write a woman as you think a woman should talk or should behave. Purge all that "a woman should; a woman would" nonsense from your head. Write a person. Write a character.

A good exercise is to write without thinking of the sex or gender of the character. Picture them like a three-dimensional stick figure and go from there. Whether it's an action scene you're writing, or a sex scene, or romance, violence... it doesn't matter. Write the scene focusing only on the characters and their surroundings. Care only that everything is functioning accordingly to the rules of the world (the rules established by the author in a real setting, or fantasy, sci-fi, etc.). 

Every time you catch yourself thinking something on the lines of "a woman here would..." metaphorically smack yourself in the head and reset. There are no set rules governing how a specific sex or gender generally behaves. Forcing your perception on your characters will likely end up removing layers, instead of adding them, making the characters flat and colorless. 

Strong female character doesn't mean one who is able to knock out seal-team-6 in one swoop. Strong female character does not mean being able to go supernova and destroy the universe. Strong means woman. 
A strong female character is one who rejoices, weeps, faces fears and overcomes them. More importantly strong doesn't mean STRONG.

Strong means real.