The idea of this training is to teach people that they need to respect someone's presenting gender without thinking it's their business what chromosomes the person has. Depending on the type of group and their knowledge base, I may do this alone, or I may do it before or after presenting basic information on terminology and resources pertaining to transpeople.
To start, I usually give a very basic two-minute explanation of the difference between sex and gender, then a very basic explanation of how transfolks might be pre-op, post-op, no-op, genderqueer, etc. I then point out that it's no one's place other than the person's to apply these terms. I emphasize the point that someone's birth sex or legal sex is not appropriate for us to define them by (i.e., totally inappropriate to do the "but she's really a he!" stuff), and that we need to treat everyone the same by perceiving them only as presenting gender (and asking for their clarification if necessary).
I don't usually get too far into genderqueer and ambiguous identities at this point, but I do a very brief mention of these identities, how they deserve our respect like any identity, and how it helps everyone to just be less reliant on binary constructs of gender in general.
So, what I do next is I ask the group, "what is my gender?" (I was born female and present as pretty clearly female). They all say "female." I ask them how they know this. They say that I use a female name, people refer to me as "she," I wear fairly normative female clothing, etc. So I tell them that they're correct, and it's therefore appropriate to assume female, unless I were to correct them.
Next, I ask them "what is my sex?" A lot of times, people will answer "female." I ask them how they know this. Some of the more savvy people might say that they've heard me talk about childhood or whatever, or heard me mention that I'm not trans. But usually, someone will say the same "your clothing, your name..." So I'll explain to them that the ONLY way they would know my sex is to look at my chromosomes. I explain that even looking at genitals isn't always accurate (and refer them back to the overview of intersex conditions and genital surgery). I remind them that there's no reason they'd have seen my genitals or chromosomes as my colleague or neighbor or whatever, so the ONLY way they have to assess my gender is based on my name, pronouns, clothing, etc. I explain to them that I was assigned "female" at birth and have never identified any differently, but again, they'd have no way of knowing this unless I told them.
Next, I'll go around the room and quickly ask the group to identify each person as "male" or "female" out loud. After we do this, I tell them that, statistically speaking, there's likely at least one person in the room who wasn't born with the gender we just stated for them. I again emphasize that it DOESN'T MATTER which person this may or may not be, because we all deserve the respect of being viewed and treated as how we're presenting today. I'll explain that there are some people who are out as trans, and want people to honor their current identity as well as their trans identity, but that this is something they'll choose to share with us. I emphasize that unless someone shares this kind of dual identity with us, we need to respect a person as how they present today and nothing more or less.
This exercise especially helps people keep track of the whole "wait, I forget, are we supposed to call trans people by their birth gender or current gender?" idea. It also normalizes the idea that transpeople are everywhere and you won't necessarily know. I tend to find that even the most well-meaning people, if they've only encountered "that one transperson on that video we saw," will tend to confuse what they're "supposed to" call that person. It seems to make it a lot easier if we go around and identify everyone as their presenting gender, instead of only doing this for the people who we know to be trans. People usually learn better if they can relate something to their own experience, and most people don't get confused about which gender label they themselves prefer.
It's pretty easy figure out what to "call" someone if I'm thinking "hmm, what gender label would seem most appropriate for someone in a skirt and high heels named Susan?"
It's so much more complicated (and dehumanizing and offensive) if I'm stuck in the less enlightened type of thought: "hmm, this person started as a guy, but now has girl clothes and a girl name, but I don't know what genitals this person has -- maybe I should ask? but you can't ask people about their genitals, can you? but you can if they're trans, right, because you need to know?"