I get a lot of people asking me how to get more people to read their work, or how to become more "popular". Now, I'm no expert...but here are a few tips that have worked for me.
1. Write What You Want to Read:
The whole reason I started writing fan fiction was because no one was writing a story I wanted to read. I had a specific situation in my head and I wasn't seeing that. So I started typing and wrote to entertain myself. Got an idea? Don't request it to someone's inbox. Try writing it yourself and see how it goes!
3. Update often in the beginning
It's like when you read a book. The first few chapters or so are setting up the story. They aren't necessarily the most interesting chapters in the book. Sure the first chapter hooks you, but there's the chore of establishing characters, plot, etc and sometimes it's a little daunting. I try to get the first few chapters up quickly so readers can become fully acquainted with the story. Bare in mind that fanfiction readers are reading MULTIPLE fics at a time, so it makes your story more memorable to them if you can get them settled in for the long haul as quickly as possible.
4. Don't go more than two weeks without updating
This one is difficult, because things get in the way of writing (jobs, school, social life, etc.) but try really hard. This is important ESPECIALLY if you're a new author. Again, it adds to your credibility and remember that thing I said before about fanfic readers juggling multiple fics at a time...it makes you more memorable if you can update on the reg.
5. Respond to Reviewers
If you engage with people, they are more likely to leave you reviews. I'm really bad at this one nowadays, but in the beginning I tried to respond to every single review I got. And on the upside, I made a few good friends by doing so!
6. Learn to ignore haters
Learn the difference between a helpful critique and someone who is just blasting you because your fic doesn't fit into their specific head canon. If they don't like your story, then leave them alone. They'll find something else. Remember rule #1: you are writing for you and also the people who appreciate you!
7. Promote your fics!
Make a graphic, gif set, quote...doing something to catch someone's attention. I've started reading a lot of fics based on how cool and graphic looks or how awesome a small quote sounded. Sometimes the synopsis isn't enough, you gotta reel in readers through another path.
8. Realize your first fic is a journey, not a destination
The very first fic I wrote only got around 100 or so reviews. Your first story may do that well, it may not. You may get 10 reviews or you may get 1000. Getting noticed takes time. Patience is the key. Don't let it get you down, keep powering through. After a year of writing I can now boast about my reader count, but back in the day it was VERY small.
9. If you wanna be a better writer, read A LOT and write everyday
Again, it's hard to do both of those things, but squeeze it in when you can. Read on your commute to work or when you are on a lunch break or in between classes. Write a few hundred words before you go to bed a night. Some days I'll write 4,000 words and some days I'll write 400 but it's important to get in the habit of practicing. It will only make you better.
I hope this helps shed some light on things. There's no sure fire, 1-2-3 step plan for getting yourself noticed as a fan fiction author. Sometimes it's talent combined with a little bit of dumb luck. These are just some of the things I've done that have worked for me :)