We'll assume for the purposes of this discussion that you really want to play a convincing female character, but haven't the vaguest idea of where to start. We will also assume that you're a man seeking to play a female character -- the advice is equally applicable for the other side of the fence, but missteps are a bit more common on this side of the fence, so that's where we're looking.
So how do you kick things off? By paying attention. By watching the characters whom you have no trouble identifying as women and seeing how they act around others.
Keep in mind that the characters in question may or may not be played by a woman. The important thing is whether or not they seem plausible to you, and more to the point, whether you would have guessed they were played by women in the absence of other information. All else being equal, we usually identify players as their characters unless we have a large amount of prior knowledge to fall back upon.
It's not that this is going to be a complicated process. In fact, it's probably to lead you to the point that I'm about to make in the following paragraph.
Focus on similarities
There's no gentle way to say this, so I'm not going to try.
Come on, guys. Come on. Every day you roleplay elves or Klingons or robots or various other species, brought up in an environment totally distinct from your own and with some distinctly non-overlapping regions. Elves alone -- do you really think you have the same perspective on life as a creature who, in most mythologies, will be a youngster by the time you're entertaining grandchildren?
And yet pretending to be a woman throws people totally off track. Somehow, the idea of changing gender puts you in a completely different frame of mind and changes every variable.
If the point that I'm getting at isn't strong enough, it's that you have more in common with the other gender than you think. Men and women both have the same basic urges, the same essential attitudes, and the same general collection of interests and dislikes. Oh, sure, there are differences, but if your character concept totally wouldn't work if you swap genders, then it doesn't work with the current gender. (With very, very rare exceptions.)
Don't spend all of your time thinking about what it's like to be a woman. Focus on the common points, the elements that are familiar. Just like you probably don't spend much of your day thinking about the fact that you're a man, women don't spend most of their day mentioning they are female.
Make them unattractive
If there's a single adjective that turns up far too often with men playing women, it's "sexy." There is nothing inherently wrong with the term, of course... but it gets used as shorthand for "wet dream."
Normally, roleplaying involves pretending to be something we're not. Far too often, playing the other gender involves pretending to be something we wish existed. And while most of us are at least a little more dashing, attractive, and skilled in the digital realm, there are a lot of characters who read like someone's personal points of attraction in semi-physical form.
Luckily, there's an easy way out of this: make the character unattractive to you. Make him or her someone you don't find terribly attractive, and if at all possible, someone you wouldn't even glance at twice on the street.
Why should you do that? Because it ties in perfectly with the whole point of focusing on similarity between the player and the character. Instead of focusing on how your character is the hottest thing on two legs, you're focusing on actual character traits. As paradoxical as it sounds, the best portrayal you can get is one in which you stop thinking of the character as a woman and start thinking about her simply as a character. Removing the vector of attraction helps.
Don't make a big deal out of it
It sounds ridiculous, but when someone realizes that his female characters are a touch unrealistic, the reaction isn't always to introduce nuance and depth. No, more often than not the entire routine becomes an unbroken string of "have I mentioned I am a woman today?" Because as we all know, most women are walking around at all times reminding people of how they have a different set of chromosomes than men.
Now, while I'll grant that it's a better unrealistic characterization, that doesn't make things any better overall. The goal is to act realistic. Missing that mark through good intentions is still missing the mark.
The best thing you can do when playing a character of the opposite gender is to not make a big deal out of it. At all. Treat that gender as exactly what it is: a trick of genetics at conception that had a fifty-fifty shot of going either way. You can't change your gender any more than you can change your hair color, your skin color, your favorite foods, or any number of other things. You got a choice when you created the character, but the character herself didn't get to choose any more than the player got to choose at birth.
Really, it's not rocket science.
As always, comments may be sent along to firstname.lastname@example.org or left in the comment field. I imagine there will be a fair number of hate-comments on this particular topic, but that's the way the cookie crumbles. Next week is once again just a bit of a mystery, so we'll see what develops.