Your story at the moment reads like the script of a play: dialogue with very little else for the reader. We can’t see the places that this action is happening so you have to paint us a picture. Also think about what you are trying to convey with each piece of the text, does it matter that Leela is reading a book? If so why? Perhaps something like:
Leela was so shocked to hear a knock on her door that she dropped the copy of Men are from mars […] on the floor. She got out of bed trying to think of the last time anyone had called on her unexpectedly; perhaps some tall dark stranger had come to whisk her away.
Her illusions were shattered the second she opened the door, before her stood the rather short, orange haired Fry…
I’m not saying that you should write it like that per se
. I’m sure that when you write the action of the story you’re thinking about how it is all playing out, you need to take that from your head and put it in the story. This is of course the hard bit.
As another little example you wrote:
But it was kind of sticky... and it didn't smell nice.
They were in the sewer.
This appears to me to be the climax of this chapter of the story so play it out a little. Describe the feeling of the “water” in their mouths, up their noses, as they plunge into it. Describe how when they finally fight to the surface they smell it, how that makes them feel, (not it “smells really bad”, make an analogy or describe the wrenching feeling when you (almost) throw up because something is so horrid.) Imagine how awful it would be to have to swim through it to the side once you knew what is was you were swimming in.
I think if you fill out the story a little like that then the reader is gonna care about the characters a lot more.
(Note: I have never written a fan fic or had any story over a couple of thousand words published, I do not consider myself the definitive opinion in writing style or technique. Take my advice with as many grains of salt as you feel fit)