Thank them. It is very hard to come out to people as transgender. They trust and/or respect you very much to have come out to you. Thank them for trusting you; it will mean a lot to them, because you mean a lot to them.
Respect their gender identity. Think of them as the gender they refer to themselves as and refer to them with their chosen name and gender pronoun (regardless of their physical appearance) from now on. (Unless they are not out, or tell you otherwise. Ask to be sure if or when there are times it is not okay.)
Watch your past tense. When talking of the past don’t use phrases like “when you were a previous gender” or “born a man/woman,” because many transgender people feel they have always been the gender they have come out to you as, but had to hide it for whatever reasons. Ask the transgender person how they would like to be referred to in the past tense. One solution is to avoid referencing gender when talking about the past by using other frames of reference, for instance “Last year”, “When you were a child”, “When you were in high school”, etc. If you must reference the gender transition when talking about the past, say “before you came out as current gender”, or “Before you began transitioning” (if applicable).
Don’t be afraid to ask. Many transgender people will be happy to answer most questions, and glad you are taking an interest in their life. Don’t expect the transgender person to be your sole educator. It is your responsibility to inform yourself. Exception: questions about genitalia, surgeries, and former names should usually only be asked if you need to know in order to provide medical care, are engaging in a sexual relationship with the transgender person, or need the former name for legal documentation. ( Matt’s note: I would say questions around genitalia are even inappropriate in some contexts when discussing sexual relationships beyond issues of pleasure and consent – it depends on the level of intimacy with your partner. Casual hook up conversations would be very different to intimate partner conversations)
Respect the transgender person’s need for privacy. Do not out them without express permission. Telling people you are transgender is a very difficult decision, not made lightly. “Outing” them without their permission is a betrayal of trust and could possibly cost you your relationship with them. It may also put them at risk, depending on the situation, of losing a lot – or even being harmed. They will tell those they want to, if or when they are ready. This advice is appropriate for those who are living full-time or those who have not transitioned yet. For those living full-time in their proper gender role, very many will not want anyone who did not know them from before they transitioned to know them as any other than their current, i.e. proper, gender.
Don’t assume what the person’s experience is. There are many different ways in which differences in gender identity are expressed. The idea of being “trapped in a man/woman’s body”, the belief that trans women are hyperfeminine/trans men are hypermasculine, and the belief that all trans people will seek hormones and surgery are all stereotypes that apply to some people and not to others. Be guided by what the person tells you about their own situation, and listen without preconceived notions. Do not impose theories you may have learned, or assume that the experience of other trans people you may know or have heard of is the same as that of the person in front of you. Don’t assume that they are transitioning because of past trauma in their lives, or that they are changing genders as a way to escape from their bodies.
Treat them the same. While they may appreciate your extra attention to them, they don’t particularly appreciate you making a big deal of them. After you are well-informed, make sure you’re not going overboard. Transgender people have essentially the same personalities as they did before coming out. Treat them as you would anybody else.