Know what fandom you're writing for:
Probably the most important factor of them all. Now if you're new to DBZ, then some thorough research would be necessary, and even if you aren't new, you still should anyway. Get to know how the characters names work, the world in which they live in, and more importantly, the time period. Seriously, do you know how irritating it is when authors give their characters real names like, Tiffany or Lisa, when in the actual fandom, all of the characters have names based on puns? A primary example would be Vegeta, since it's 'vegtable' without the last three letters. As for the world itself, I always see writers including actual countries into their stories, which is truly baffling, since the whole world is just one big country in DBZ. Big turn-offs for me, so avoid this, people.
Avoid OCs that are related to the Canon characters, especially the Saiyans:
Unless she/he is the child of any of the Demi-Saiyans (excluding Gohan), or Pan. Honestly, do you know how many times I've come across OCs that are Goku's Half-Saiyan daughter, mostly in Trunks stories? It's the same thing, over and over: She either travels back in time with him, or ends up being his childhood friend, as well as Goten's twin sister. And it really doesn't help when her name isn't a pun, or has physical traits that don't match any of her parents, either. And also try to avoid any connections with Dr. Gero; creation or child. It is truly annoying to see another Android who is more powerful than Cell himself, or some daughter who hates what her father does, and helps his enemies instead.
Do not make your character stronger than any of the Z-Fighters or major villains:
Another Mary-Sue trait I see is when authors make their characters equally matched or stronger than Goku, or any of his Saiyan brethren. Bad move! It's even worse if she's more powerful than Cell, and can ascend to Super Saiyan level or higher with pure ease. Also, if she is trained by someone, don't give her all of her mentor's moves. One or three minimum is fine at best, but be sure to give her some of her own unique techniques. Be creative.
Don't let them have the spotlight all the time. Give their Canon pals a chance to shine, too:
A story that has the plot and everything entirely focused on one character, without giving any of the Canons their feelings or thoughts, is one of the worst mistakes possible. If you want to make the story more interesting and believable, let the Canon characters give some input onto what is going on. How are they feeling? What are their thoughts on the matter? Almost everything in DBZ is a team effort when something goes wrong. Having everyone work together to solve the conflict in the story is a great step into making everything more realistic.
Give them flaws, enemies, rivals, and avoid everyone liking them:
Now, it's pretty painful to see an OC who is instantly fawned over, liked by all the characters the author likes, and hated by the ones she doesn't. To avoid this, balance it out a little. Have some characters like her/him, even the ones you aren't fond of, and ones that just see them as a comrade. Also, try not to make them perfect in every way, as this also goes hand-in-hand with being stronger than the Saiyans. That means no perfect figures either. If she/he fights and trains a lot, they can be toned and fit, but no 'curves in all the right places' and perfect breasts. And make sure they don't have perfect hair or 'soul-piercing' eyes, either. Make sure they have a balanced amount of flaws and good traits, strengths and weaknesses, and fears and habits. As the saying goes, 'Nobody's perfect', and your character is no exception.
Do not rush the romance, or have them pair up with a character in a already established relationship:
One of the things that irk me to no end, is when an OC and her Canon love interest fall in love at first sight, or become too close too soon.For example,we all know Trunks from the future timeline is a nice guy, but I highly doubt he'd trust someone so easily, or jump into something right away with no previous experience on dating. Love takes time, so don't rush it. More importantly, whatever you do, please do not break up a marriage between two Canon characters, so that the love interest in question could end up with your OC. Not only is this annoying, but it completely goes against Canon, and many people will dislike you for it. Other than that, feel free to pair them up with someone who doesn't have a spouse, but like I said, take it slow.
Don't bend the rules of the Universe for your character:
Yet another face-palm worthy trait; When writers will deliberately break the rules of the fandom to make something that was previously impossible-possible-for their character. One noteworthy example would be having a Quarter-Saiyan character to ascend to Super Saiyain level, when Akira Toriyama himself has stated that Saiyans who are only a quarter or less, cannot ascend to this level, due their more dominant human blood. I know what you're probably thinking here: "Well, they aren't any female Super Saiyans, and you told us not to make anyone related to the other guys, so what do I do?" Well, the answer is very simple; you can probably get away with having your character make a wish to Shenron or Purunga (depending on which timeline you're writing for) to reach this extraordinary level of power. And seeing as the Dragonballs can grant even the most absurdest of wishes (one being immortality), it could be possible. However, keep in mind that the Earth's Dragon was not able to make Android 17 and 18 human, but then again, Shenron is not as powerful as Purunga, who is able to revive a person more than one time, within a certain amount of years after their death.
Avoid making Pure-blooded Saiyan characters:
So you think you might be able to have a great Saiyan character who is not related to Ratiz or Broly, and is from an entirely different family of her own. Okay, cool. But there's just one very, major problem: Frieza obliterated Planet Vegeta, sometime after Goku was born. So, how did she/he survive? If I or any other DBZ fan can recall correctly, there were only very few survivors, and most of them ended up dead, leaving Vegeta, Goku, and Tarble as the only Pure-bloods left. The only possible you way you could probably get away with this, is if she/he lives in Other World, after their planet's tragic fate, where they train, fight, and reach Super Saiyan level. Just keep in mind that they are permanently dead, and will never see the light of any other planet's day again. Now, You see, there's a very good reason as to why the Saiyan race is extinct and exclusive to only a few survivors; they were the strongest race in the universe, and having so many would be a threat to a lot of people. Don't forget it.
Avoid making a Self-Insert:
Do I really need to elaborate on this one? Not only is it very Mary-Sue-ish, but it's also very annoying and will make you out to be some pathetic fangirl who only has a character made for wish-fulfillment purposes. Please, no more you getting sucked into DBZ, or becoming a Saiyan. Just no.
Don't rush the plot and make everything easy for your character:
If you want a believable story, make sure your character doesn't accomplish a lot, or get close to any of the Canon characters in a short amount of time. Also, don't make them reach any of these goals with ease; give them lots of trouble, because it will be all worth in the end, for you, the author, and your character.
Well, I guess that's really it. Now, please don't be offended. I had originally planned on writing this after being fed up with the amount of poorly written Trunks/OC stories on FF.net, so think of it as something that I'm venting my frustration on. Anyway, I hope you found this really useful and helpful. =D
-Reiko