How to use fanfic to improve your writing
Fanfiction gets a bad rap, but it's still practice writing
There's that fuzzy legality of writing fanfic--it falls somewhere between stealing ideas and fan art, and that makes people look down on it. There's the snobbery of "you're not even using original characters". There's the snobbery that mainstream writers like to throw on everything that isn't also mainstream, especially genre stuff, which inspires piles of fanfic. There's the fact that it's predominantly a women's hobby, which makes people dismiss it, like knitting or cooking or whatever.
Buy you know what?
Fanfic is still writing. It takes all the same skills and many of the same disciplines as writing original stuff, and it's often a safer and more feedback-full place for new or unsure writers to practice without that vaccuum that can happen when you're only writing your own stuff and you don't know any other writers.
Here's some ways it helps you be a better writer...
1 - It lets you learn to take criticism
One of the hardest things to do when you're a new writer, is let other people read your stuff. There's a tendency of keeping it too close to your heart, so that when people say something isn't working or that something doesn't make sense, it feels like a personal attack--even though it almost never is.
But fanfic is inherently public, so there's less of that fear because you know from the beginning that people out in the world are going to be reading it. It's easier to find beta readers and get straightforward and non-aggressive critiques. And when you get them, since fanfic is so collaborative, it teaches you how to apply that criticism to make your work better.
Once you've mastered those skills, you can apply them to your personal original work and be less afraid--and more open to ways to improve those early drafts.
2 - It helps you figure out dialog
Dialog is often one of the hardest things for writers to handle. But fanfic has the benefit of the actual existence of people who actually talk. Outside your own head, and in very specific ways that we-the-writers don't have to come up with on our own.
That detail means that when we write in the actual voice of the previously-existing character, we're learning how people talk, how sentences are constructed, how conversations happen (hint: not really in straight lines--people talk over each other and talk about different things and try to dominate discussions, etc etc etc). Writing in the voices of difficult characters who are a lot different from ourselves and our own characters helps widen perspectives and enrich our understanding of real people and fictional possibilities.
When you take that skill back to your own writing, it can't help but make your conversations richer and more real and natural.
3 - It helps you figure out plotting
Whether you're a pantser or a plotter by nature, at some point, you'll look at a work and go "what the heck is going to happen next?" When you're writing fanfic, you also have the added nudge of having people waiting for it, and hoping it makes sense in the end. And you're making sure that the parts feel complete, that the breaks happen in good places, that the story is logical enough to hold together, and that the arcs all make sense. Whether you're writing one-shots or chaptered fics, there's a basic element of plotting that teaches you how to construct stories.
The fact that most fanfic writers are also fanfic readers also helps, since the more you read in general, the more knowledge you have on plot and story structure. Even bad fics can help with this, if you can identify what it was that makes it bad to you, and why it's something you wouldn't do.
And then apply that conscious study to your own original writing.
4 - It teaches you followthrough
This one is also because of those people waiting for the next chapter and offering feedback--when there are actual people involved, it's much harder to drop a story, and much easier to actually reach the end, something that can be very difficult when you're writing alone with no feedback along the way.
One of the best ways to just automatically improve your writing is to finish stories. As many as you can. Fanfic encourages fast updates, quick writing, and followthrough, all very useful skills for a paid writer to have and to use.
5 - It's intensely interactive
And fundamentally collaborative.
Fics will get feedback. They'll get shared. They'll get inspired by others and will in turn inspire future fics. There are piles of challenges where writers will create a lot of small stories in a short time, or will write on prompts, or will gather their favorite stories for others to read and love. There are teams who take turns writing stories together.
And there is little to no wall around the stories--original fiction is guarded, but fanfic is already a little transgressive, already breaks out of the boxes that traditional stories get put in, and therefore it's freer to be cross-pollinated and more openly inspired by other works. Works will be written in response to the same prompts, or will be different takes on the same ideas, or will be answers to each other, and there's no law or convention that keeps that from happening the way there is in traditional, fully original writing.
Because of this, writers can try on lots more ideas, styles, characters, story lines and story constructions, collaborations and partners, than a traditional-only writer might be able to do. All of that fast-tracks skill-building and makes for a flexible mind that can create more original stuff of their own.
So give fanfic a try
Even if you never share what you write, and skip the interactive parts of the experience, it's still practice, and all writing practice is good practice. As long as you're not making money off of someone else's characters, and not stealing other fic writers' ideas, you're going to be building the skills you need to be a better writer.