Almost every week, I come across a blog post or an article requesting more stories starring Blacks, Asians, Gays (or anyone else in the LGBTQ group), fat people, developmentally-challenged etc, etc. (For the purpose of making both our lives easier, I'll call these populations The Other from here on.)
But before you rush out and do the noble thing of writing about one of the populations, let me tell you something that every Black, Asian, Gay, fat person, etc, and all their friends know. There really is no worse disservice to these populations than a stereotypical character.

I don't profess to be an expert. I don't think that, because I'm black, I have more knowledge on this topic than anyone else. But I am innanely fascinated by the way people work, so I'd like to give you a few things to consider.
1. The Other is not just The Norm, but with a twist.
A few weeks ago, I read a blog which referenced a post on writing LGBTQ characters. One of the schools of thought was that these characters should be written "just like any other character, but gay". I agree with the blogger that this is entirely not true.
The Other is always different, as long as they live in a society where The Norm is revered/more accepted. A character is not totally unaffected by the fact that she is fat. If there's a beach party, she will probably be more reluctant to come out in a bikini. I remembered thinking about this recently, as I re-watched Dawson's creek. Joey was in a bikini every episode. A fat character would never do that. Growing up on a coast/creek/lake or in a community where everyone has a pool must be a nightmare for fat teens. (Little kids care a lot less.)
2. What it means when The Other acts like the Norm
Maybe you know someone who doesn't act like The Other; doesn't seem to have the same hangups of people in their group.
If you want to write characters like this, you need to know why they act like The Norm, and to understand what it means to them to act that way. Is your Black character not like other Black characters because, like me, she grew up in a non-stereotypical Black community, where she had Black role models and access to education?
If your fat character puts on a bikini, it means something different than when a 90 pound character does. Maybe she's supremely confident and self-assured. Maybe she's tired of being bothered about what other people think.
3. How does The Other react when in a situation where The Norm is King
Things don't go as right for The Other as they do for The Norm. The Other is often discriminated against. We're used to the 'big discrimination': not getting jobs, not getting promotion, not being picked for teams/clubs in school. But The Others can also experience small acts of discrimination. People don't smile at them as much. Fewer people want to be their (girl/boy)friends.
People react to the discrimination (real or perceived) in different ways.
There are some people who take it as a personal affront and blame everything that goes wrong on it. ("It's because I'm Black, ain't it?)
Others refuse to fit the stereotype. They aspire to reach all the places they're not supposed to.
Others ignore the expectations.
4. How do The Other's micro-society's standards fit with those of the society at large
This is a big consideration for people who grow up in Jewish, Japanese, Korean, Chinese, Indian, etc, families. They may be expected to get all A's at school, whereas their friends are allowed to just pass the classes. They may be expected to have an arranged marriage, while their friends get to choose their partners. The may be expected to marry their first SO, while friends can date casually.
Some people deal with this like it's just a fact of life. For others, it's a severe trial.
5. New-found Other status
Life is also significantly different for those who grew up in a situation where they were not a minority.
What's life like for a recent immigrant? Who must suddenly deal with getting strange looks and people who ridicule their customs or insult them? What's it like growing up in one of the niches of America where minorities aren't minorities (San Francisco, Atlanta) and then moving to somewhere else?
These are just a few of the things that pop into my mind on this topic. If you're going to be bold enough to write an Other character, be sure to consider all the ways in which being an Other may affect him or her, and, just as importantly, how it doesn't. Think it through. Do your research. Find an Other (or, in the case of some developmental-disabilities, someone close to an Other) and talk to them. Ideally, let them read your work and give you feedback.
(Hilarious blooper. "I don't think that, because I'm black..." originally read, "I don't think because I'm black" Thank God for proofreading! lol. I know some black people who would so not have not been thrilled with me.)