Most people don't act sexist in real life, but it's easy to accidentally work an insulting and potentially harmful message into a work of fiction. Here are some tropes to consciously avoid.
A man hitting a woman is scandal, but a woman hitting a man is funny¶
This is easily the most offensive single trope on the list, especially because it's not confined to the realm of fiction. The more we portray this as okay in stories, the more it becomes "socially acceptable" in real life, and the more innocent men get physically assaulted and feel like they don't have a right to defend themselves. So for real life victims' sake, don't make your female characters sexists that abuse their one-sided social power in this area. If there's a good reason to have such a sexist character, portray her as such; the woman who does this should be a villain, or receive a response in kind from a non-villanous victim.
Fathers are harsh, mothers are loving¶
I can already hear you starting to say "But I have statistics here that validate this trope". No, it doesn't matter if it's statistically accurate. Even if trends like this do exist, we ought to portray them as false in fiction, because that helps erase double standards - it provides an example of a loving father so that real fathers don't feel like it's somehow natural or right for them to be the strict one and leave compassion to their wives.
Some writers seem to try to avoid that result by taking it farther and making the dad an outright villain. That might be less actively harmful in the sense that it doesn't glorify bad behavior, but it's even more insulting to real life fathers. I think we've all seen enough of the "strawman chaotic evil sadistic dad" trope.
The 100% male cast¶
The most obvious way to be misogynist: just put very few or no women in the story. Look no farther than some of the Assassin's Creed games for a perfect example of this. In the historical past of the games (which is where most of them takes place), the first game has exactly one notable female character, and she is in exactly one scene. Assassin's Creed: Revelations has one female character also, and she is a rescued love interest. Assassin's Creed 3 has exactly one significant female character, and she dies to motivate her son (see below) when she really should have just been the protagonist of the story honestly. Unless you have a specific reason to make an exception, about half the characters should be female.
As for other examples, the Greybears in Skyrim and the guards in Oblivion are all-male for no reason; it's especially pointless in the case of the Greybeards, who are not even fighters. It seems to be only that the writers based their ideas about the Greybeards on real-world priesthood, which is all-male for many religions, and so it may not have even occurred to them to do anything different. While Mistborn is a mostly non-sexist story, there's still no real reason why there's only one female member of Team Good out of like... 8 of them? I guess they add Tindwyl in book 2, along with about that many more male characters.
The damsel in distress¶
The trope that women can't hold their own in the game of fiction and need to be rescued by men all the time. I've written some tips on how to handle rescues better.
I don't think I even need any examples for this one, but some that stand out to me include keeping Asuna hostage for something like a dozen episodes of Sword Art Online; The Mortiis episode of The Clone Wars where Ahsoka is captured by The Son and the writers make her totally break character to act as pathetic as possible; AC Revelations.
The all-male family¶
This one would be funny it wasn't sexist. A lot of writers don't seem to realize that you can't have a father and sons without a mother. No one ever even asked in the Clone Wars arc that featured this trope (albeit that family had a daughter, still an instance of the trope). Sometimes there's at least a handwave - usually that the mother is dead - but even then it's still a questionable excuse to avoid having female characters in the story: remember that everything in the story that needs to be explained must be so for a reason - otherwise you're wasting time - and so there should be a mother unless there's a good reason not to. If you have a good reason to want only one parent around, remember it's an option to have the father be dead, and it's better to be symmetric by reversing it every other time than to default to the mother being the dead one.
The female love interest or other supportive character is martyred to motivate the male hero¶
This happens in Sword Art Online (with Sachi), The Force Unleashed 2, Star Wars: Revege of the Sith (it doesn't literally do what I said but it uses the threat of Padme dying to motivate Anakin and then kills her by complete Death Ex Machina after Anakin turns evil), and in Beneath A Steel Sky, to name some examples. None of these female characters were killed for the sake of their own arcs; on the contrary Padme's arc was ruined for it, Juno (TFU 2) had literally no other role in that story even though she was a major character in the original, and the same can almost be said of Anita (Beneath a Steel Sky).
I - and I believe most men - wouldn't like it if male characters got this treatment as often as women do, so let's not always do it the opposite way. You really shouldn't martyr a character of any gender unless it's the best conclusion to their own arc.
Asymmetric treatment of nudity¶
Men are almost never seen naked in fiction. But female nudity is everywhere, whether it's used to take away the character's dignity (as with princess Leia in Episode 6) or to make her sexually attractive to a presumed male and perverted audience (as with queen Ming in Lost Odyssey, or with just about every female character there was in Sword Art Online). In fact, this double standard exists in real life too: men's formal wear covers their entire bodies modestly, whereas women's tends to be very revealing, particularly at weddings.
'Lady' is used to talk down to women¶
For some reason 'lady' is almost a derogatory term in some cases. Consider the following scenario (this is pretty much something that happens in Mass Effect 2 and that the player isn't given a choice to even object to): a woman returns to her house and finds that the police are searching it and there's a guard by the door that won't let her in. She argues with him, but he says, "The law is the law, lady. You can't change it." That sounds natural, doesn't it? But what if the genders are reversed and the guard says, "The law is the law, man. You can't change it." That sounds weird and makes us think, "is there something wrong with being a man?" and rightly so.
Grossly exaggerated physical power gap¶
Not too much to say. Sometimes even stories that don't use a female character as a damsel in distress do this, like the Doki Doki Literature Club mod A Brand New Day where girls sit out a fight they could be helping with, though that example could also be framed as misandrist.
Women need help with basic physical tasks¶
I really hate to say it, but Doki Doki Literature Club is going to have to be my example here. In an optional scene, the following excerpt takes place:
"Sayori hastily bends down to pick up the piece she dropped."
"But being inattentive of her surroundings, she bumps right into me."
MC: "It's fine, it's fine."
MC: "I'll get it for you."
"I bend down and pick up the broken pencil."
"Sayori clutches the desk beside her to support herself, knees shaking."
Sayori: "I-I'm a little clumsy today..."
MC: "Let's sit down, Sayori..."
"I grab Sayori's arm and help her sit at the desk."
I get that Sayori is clumsy, but does she really need help with picking up a pencil and sitting down? 1-year-olds do those activities on their own.
Men are just, women are kind¶
This is distinct from the misandrist trope that fathers are harsh and mothers are loving, because there the implication is that one is good and the other is bad while here the implication is that both are good, they just specialize in different virtues. And there's nothing wrong with that in a vacuum, the problem is that it's a cultural belief - many people actually think this is built in to our biology. We could use some stories that invert the stereotypes to erode that belief.