Every time I finish a chapter or a oneshot piece, I sweat. My stomach aches. My hands shake. It doesn't matter if I'm about to post a 5,000 word installment of my latest epic or a 500 word installment of Vader's Cat. It happens because the story is mine. It's part of me. I'm sharing something that is integral to who I am. I'm putting it out on the internet for anybody to come along and pick it up and potentially hate it.
What if they hate it this time? What if I disappoint them? What if nobody's even reading it anymore because it's been so long since I posted the last one?
If some variation of these thoughts don't run through your head--even for a second--just find another hobby. I'm not joking. If your story doesn't mean anything to you, I don't want to read it, and neither does the rest of your fandom.
However, if your story does mean something to you, and you click that submit button anyway, congratulations. You are made of awesome. You've done something that most people out there never have the guts to do. Even if you come back to your story in a month or a year and decide you don't like it, you're still awesome for taking the risk.
You should know that if you stick around in fandom long enough, you will eventually accumulate a stockpile of cringe-worthy early material. Leave it online.
On a related note, if you are reading someone else's fanfiction, you should leave a review. You don't have to leave one for every single chapter of a long fic (although the author will most likely adore you if you choose to do that) and you don't have to say very much.
Some people have a hard time coming up with things to say in a review. I hear them say things like "I don't know what to say, and it feels dumb to just post "I liked this." As a fanfic author, let me say, you will not sound dumb. You will sound like the entire angelic host come down to deliver me a personal piece of encouragement.
If you have negative feedback, leave it. That author is never going to improve if all he or she hears is "OMG, this is amaaaaaaaazing, plz more!" I am a pretty blunt reviewer; I say things that are honest and I tell authors both what I did and did not like about their stories. The key is to leave constructive criticism. That means, if you have a negative comment to make, give the author a reason for your statement and (if at all possible) a suggestion for making the story better. Vague one line statements of what a reader didn't like don't help much.
I can't always think of something to say either. Some of the pieces I read are so bad I want to bleach my eyes after reading them. The last thing I want to do is say "Thanks for posting this." I say it anyway and leave a couple of suggestions, because I have gone back to the work I wrote when I was first starting and I have cringed. I know what it's like, and I know that even the most horrendous author can improve over time.
If you're reading something so bad you just want to click off the page and forget you read it--don't. Go the review box anyway. Type something. You don't have to lie. "Thanks for sharing." It takes a total of three seconds. Call it collecting karmic points.