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first i think you should ask your friend who they’d like to be out to, and who they’d be okay with you using their pronouns around. like if they don’t want certain family members of theirs or yours, or some strangers or like, teachers or classmates, etc., knowing about their gender and pronouns, then talk to them about it and come to an agreement of when to use their pronouns. and also what pronouns to use in situations where they don’t want to be outed, and how to navigate those situations in a way that they’d prefer. i think that should take care of most of the situations!

if they definitely do want you to use their pronouns in all situations (or most of them), then i think there are a few helpful and safe things to do 

first off, here’s some reassurance that usually, people rarely ever notice when you use they/them pronouns for people in conversations. they also rarely ask for clarification or point it out. 

so if you use they/them pronouns for them, and no one asks, BUT the person you’re talking to doesn’t pick up the use of the pronouns (and they use other pronouns for them), then it depends on the person. 

if you know they wouldn’t be receptive, just leave it be and keep using they/them pronouns. hopefully it will go unnoticed.  

this is the direct answer to the question you asked: if you think they would be receptive, i think the quickest explanation is, “[my friend] wants to have people use they/them pronouns to talk about them. so it’s like in place of him or her.” if they accept that, great! if they require a little more, say, “they just don’t like being called him or her. it’s a comfort thing, so i’m using they/them pronouns to respect them.” i wouldn’t bring gender into it unless they do first in a respectful way. if they ask “is it because they’re not a boy or girl/they’re non-binary/trans” i think it’d be fine to confirm that! anymore information would be beyond your scope since you’re not your friend. although asking your friend for how much information to give is okay, would be very good/helpful!

if they DO notice you’re using they/them pronouns and you know they wouldn’t be receptive, and they notice if you KEEP using those pronouns, then probably just avoid using pronouns or change the topic. 

so to sum up:

ask your friend when and with whom to use their pronouns! ask about possibilities like with specific people, if they ask questions, and what pronouns to use if they don’t want to be out. always get their permission for outing them to certain people if it comes up in conversation.

if you’ve cleared it up with them and they’d like you to explain, they could help as well! but the quickest way is probably an exchange like this:

why are you calling them they? are you talking about more than two people?

oh no, i’m just referring to [friend]

so then why ‘they’?

because they don’t want to be called him or her/they want us to call them by they/them pronouns, in place of him or her. 

why?

it’s a comfort and respect thing. i’m respecting their wishes. 

is it because they’re nonbinary or something?

[IF YOU HAVE PERMISSION TO CONFIRM] yes, it is. ANYWAY as we were saying blah blah blah

BONUS:

if you want to explain what non-binary genders are, my go-to is always “not a boy, not a girl, just kind of a person”

if they ask about genitals, about surgery, invasive questions, or use slurs like h*rmaphrod*te or something like that, then this is a good response:

“no no, non-binary genders don’t have anything to do with that. those are also invasive questions/offensive words, please don’t ask/say them. this is just about respecting their wishes.”