Allyship to trans people involves a number of different actions: some are necessary and relatively easy, while some require more commitment and activism. I will make several lists in order of priority. Some of these are behaviors that you must engage in to treat trans people respectfully; some are goals to aspire to, but they may take a while and require some more courage!
Call people by their preferred name, pronouns, and label. Always. Even if you're angry with them, even if they're total jerks, even if they're using gender-neutral pronouns that "sound weird" or "are hard to remember." Yes, even when they're not around to hear. It's a respect thing.
If you've met the person after transition: don't ask to see pictures from "before," or ask about their previous name, or otherwise quiz them on topics that are likely offensive/painful.
Don't try to compliment people by telling them that they look like a "real [gender]," or that you "never would have known."
Don't make comments about the person's gender presentation that you wouldn't make to someone who was assigned that same gender at birth. Critiquing a trans woman's makeup in detail, or offering a trans man suggestions on how to walk "like a guy," is as rude as it would be if you were talking to a cis person.
Do not inform any third party that your sibling/parent/partner/whomever is trans without the trans person's express permission, gotten in advance.
Don't describe past situations by saying "When [person] was a [gender]. . ."
Don't ever describe someone as a member of the wrong gender, even in a way that's superficially nice. "But you're so handsome as a man!" is unacceptable, as is "You were a lovely little girl."
Words that you shouldn't ever use: "tranny," "shemale," "he-she," "shim." Seriously. Even if your other trans friend told you it was okay. Just don't say it.
Don't make comments that fetishize trans people. "I love trans guys — they're so hot!" is pretty belittling; so is "People like you are so exotic." These kinds of statements reduce trans people to sex objects, as though we exist just to be that "exotic" kink or turn-on.
Don't ever ever inquire about the state of someone's genitals, about whether they're having surgery, or about how they have sex. Ruuuuude.
Don't make assumptions about someone's sexual orientation. Some trans men are gay or bi, or asexual; likewise with some trans women. Genderqueer folks have sexual attractions that come in all stripes.
Yes, it is certainly difficult to adapt to thinking of a person in a new way, particularly if you've known that person all your life. A period of discomfort, or even mourning, is not uncommon. But I challenge you to try to work through that — to understand that trans experiences are usually much harder for the trans people themselves — and to work earnestly on understanding, rather than becoming bogged down in regret.
Many aspects of these concepts can be confusing or difficult at first. (Maybe your trans son is still in a relationship with a lesbian . . . why? Maybe your trans sister chooses not to have surgery, though she could afford it . . . why?) However, most trans people do not wish to serve as constant educators; being asked to justify your choices, some of which are so instinctive that they're beyond words, is tiring and draining for everyone. Be sure to think over your questions carefully, seeing if you can answer them with your own common sense, before you ask the trans individuals themselves.
If you're in charge of a public bathroom of some sort — in a store, perhaps, or a university building or a workplace — you may wish to label it as unisex or "family." Some, though not all, trans people are not comfortable or safe in either exclusively-men's or exclusively-women's facilities (maybe they're pre-transition, maybe they present as androgynous and don't want to be hassled). It's not a big deal to put up a new sign, and it makes sense for reasons beyond trans issues; young children, for instance, are more easily able to enter unisex bathrooms with their other-gender parents.
Keep in mind that a gender-neutral bathroom should not be used to segregate trans from cis, but rather exist as a voluntary option. It'd be inappropriate to say "Trans women in the genderless lavatory, cis women in the women's lavatory"; that sort of phrasing implies that trans women are different or unreal.
Refer to "all genders" or "any gender" (plural) rather than "both genders" or "either gender" (dual). Gender is not a salt-and-pepper set, with only two condiments on the table, if you want to think of it that way. It's a much larger sort of system, including the possibilities of "male" and "female," but not excluding anyone else either.
Occasionally — when you're on the subway, maybe, or driving past a pedestrian — you'll see someone whose gender you can't decipher at first glance. A total stranger, not someone whose identity you actually might need to know. Your instinct is likely to take a closer look at the person, closer than you normally would, and try to figure out what gender they are. Avoid this, if you can, or at least stop yourself consciously in the midst of doing it. The person may not know the wiser, unless you're outright staring, but this is an example of an invasive and transphobic behavior. It's not the King of Indiscretions, but it needs to be treated seriously: you'd feel insulted if you were scrutinized in such a way ("is she or isn't she?") and so will most other people.
Trans people are not freaks. The label of "freakishness" can go either way: people may see it as something repugnant, creepy, or against nature — or they may consider it exotic, or especially erotic, or radical.But transness is none of these things. It can't be so easily characterized by that kind of shallow stereotype. It isn't something super-special to be considered "cool" and "fascinating," and it isn't something super-gross or weird or barbaric. It's just a Thing, a fact of some people's existence, and when you assign it a moral meaning the actual facts can get lost in the theory.
Try to level out your thinking on trans issues, realizing that it's more complex than either an "awful curse" or a "special gift," but just is. ... Some people, individually, will choose to embrace a freak identity. But that has to do with their individual journeys, rather than encompassing all of what trans means to everyone else.