Mainstream culture embraces a gender binary, or the idea that there are only two genders, men and women, and that a person must fit into one of these two labels.
I recently had the opportunity to talk with a trans woman about her experiences with a group of people working on the Vagina Monologues, and she told us the perfect metaphor about passing gender.
I don't have the exact quote, I should have written it down, but I honestly wasn't preparing to write anything about the conversation we all had. However, I do remember the basic idea behind what she said.
She said that it's like people walk around with a checklist in their heads. The checklist has two sides, the two sides of the binary, and their mainstream stereotypes for each gender (men have lower voices, women have less body hair, etc.). She said that when someone meets someone for the first time, they check off the qualifiers for the gender in their head, and whatever side has the most checks, is the how the person genders you.
This kind of blew my mind as to how gender stereotyping actually works. I think it's really accurate. And clearly, it's very harmful.
Don't gender people. Don't assume you know how they identify. It can be harmful and hurtful to them.
The easiest way to not gender someone verbally is to use "they" pronouns unless otherwise informed by that person. And, if you do misgender someone, don't make a big deal out of it, apologize, correct your language and move forward.
I need to add a mandatory I'm cis gender notification here because trans representation comes from the trans community first, and my voice is less important to hear as an ally of the trans community.
Here's a good link to trans voices and resources: http://www.theguardian.com/lifeandstyle/2012/nov/29/transgender-advice-best-resources-online
I haven't checked them all out individually, but it seems as good a place to start as any.