Write without using someone else's characters or setting. It makes you a stronger writer.
Ignore people who tell you that fanfic writing is lazy, uncreative, weak or not "real" writing. If it's fun for you, that's the most important thing.
Author's notes: keep them brief, and keep them to the beginning or end of the chapter - not in brackets in the middle of the text. Here's an example of what I'm talking about:
Bad Fanfic Writer said:
"I want to be everybody's friend everywhere!" said Gentaro. (A/N: LOL isn't he funny!)
Yeah. Don't do that. Also, do not have conversations with "muses" in the author's notes.
Spell check and make sure to get the names of canon characters, mecha, attacks, etc. correct. Be careful of mixing up names that are similar to characters from another series - like calling BoukenYellow Natsumi or MagiGreen Mikoto. It gets confusing for everyone.
Avoid what's known as "fanboy" or "fangirl" Japanese: random Japanese words dropped into the text. It's OK to use words like henshin or -san or -chan that we wouldn't generally translate, but don't do this:
Bad Fanfic Writer said:
"Ne, Hiromu. A Megazord has just arrived. Kowai ne!" said Yoko.
"Daijoubu. We will defeat it with our badassery," said Hiromu.
"Demo, we haven't taken down the Metaroid yet. Hayaku! We have to finish this!" said Ryuji.
I see this in a lot of tokusatsu fanfics. It just looks bad.
When writing dialogue, think about whether you can actually imagine the character saying it. If not, try to rephrase it. Also try to make the character sound like a normal person and not like they're reading lines from a script (unless it is appropriate to that character, e.g. GoseiKnight)