It sounds simple, but it still gets overlooked.

The classic 'tenth walker'-style Sue will join up with the canon characters and go through their adventures, because that's what the plot of the canon was. And the canon characters will allow them to do this because that's what the fanfic plot requires. Regardless of whether allowing a stranger to tag along is a good idea, and sometime even with the stranger having no real motivation to join up with them. Motivation is an important part of characterisation.

Sues have previously been described here as 'unintentionally flat' characters. I.e. characters with no depth beyond a bare minimum. Some Sues have a tendency to be nothing more than physical descriptions with a collection of powers/abilities. Flat characters aren't necessarily a Bad Thing - they can be useful in certain contexts: the faceless masses in the background, the NPCs populating game towns so that they don't look deserted, etc.

If your characters are in a bar, and they mention the barman, that's probably enough detail and characterisation for him (as long as he exists just to serve the other characters their drinks). A physical description could add a bit of flavour to the scene, but isn't always necessary. You can get away introducing background characters just with the role they are playing in the story - you can't get away with introducing someone as 'the/a protagonist' and expecting your readers to take your word for it.

They need a reason for what they do, and they need to react believably to the things that happen to them, and the people they encounter. Also, the people that they encounter should react believably to them (when they don't, PPC agents start talking about people being thrown out of character).

It's hard to have a decent character without having characterisation. Think about their likes and dislikes, their hope and fears. And think about why they do what they do.

If their reactions to story events are dictated by the requirements of the future plot (or in the case of tenth walker style stories, the requirements of someone else's future plot), then those characters are pretty weak (in narrative terms, nothing to do with physical strength). If, on the other hand, their reactions are dictated by their personality - they do those actions / make those choices because that is what they would do, then you've got yourself much better characters.

Exactly what makes a Sue is a very complex topic, so avoiding Sues is a fairly complex task. And there are plenty of other things to consider outside of the stuff that I've just talked about, but giving a character a proper personality is a damn good starting point for ensuring they don't end up a Sue.

- Irish

Honestly, this is the kind of question that doesn't have a single answer. While extremely obvious Sues are fairly easy to avoid - don't make your character the best swordsman ever or so beautiful it's a curse - these are in the end the symptoms, not the cause.

A few random tips:

• Let your characters be hurt by their flaws. Frequently Sues will have flaws that make them appear "cool," such as a bad temper or a tendency to mouth off, but they'll never get unjustifiably angry or insult the wrong person.
  
• Don't be afraid to let bad things happen to your characters or have them make mistakes. Coddling can easily turn a well-written character into a Sue.
  
• Try not to take any criticism of your character personally. This can be especially hard if your character tends towards self-insertion, as it can sometimes feel like a personal slam. But getting indignant on your character's behalf will only hurt your ability to develop them.