I think the first thing that needs to be addressed is who this exposition is for. Like, is this just for the readers to understand a world that the characters already know everything about? Or are there characters in the cast that need to learn, too? It's a really important distinction...
When it's only the readers that need to learn, exposition is a LOT less of a big deal. Or maybe it's actually a bigger deal...because that's when you need it to look as natural as possible, and I can see how that might be difficult.
You want everything to look like normal speech...you don't want the characters to say things like "here we are at our base"; they all already know what it is. You want them to say things like "let's just go back to base" and simply go there.
Similarly, you don't want to use a lot of
* team leader stands up * "As you know, [insert GIGANTIC info-dump spending an exorbitant amount of time on things the team members already know, with just a smidge of new information at the end]"
...that kind of stuff. You could probably get away with it; lots of writers do it (especially in anime). But I find it very logic-bendy and kind of lazy, and I know I'm not the only one. If I'm already feeling iffy about a story, one of those is usually my ticket out the door.
Basically, teaching readers is about showing. You want them to learn by watching what the characters do and how they talk about it.
Dialogue is very important for revealing names and other technical details...for example, "Hey, [character], I need to borrow your [futuristic vehicle]." "Why, did you forget to put [futuristic fuel] in yours again??"
Or something a little more silly and obvious, like "How are we ever going to defeat [evil alien overlord] if you cadets don't get your act together?!" You can teach readers a LOT just with short, casual interactions like that.
Now on the other hand, when you have a character in your cast who needs to learn (especially when they're an MC) that's when things can get dicey. You can easily fall into the trap of "well, they won't learn unless someone tells them, so this 1,500-word info-dump is necessary for the story". No...it probably isn't.
Restraint is your best friend. Figure out what the character absolutely needs to know in order to do what they're doing next in the story (yes, they should still have a task/objective in mind; real life does not set aside time for tutorials) and limit explanations to covering just that. You should not lapse into lessons about the culture of [fictional race] in the middle of explaining the battle plan.
Furthermore, let the character's questions drive the discussions. If you DO want to talk about the culture of [fictional race], have them ask what another team member's tattoo means, or why the buildings they're walking past all look a certain way.
Restraint is necessary here, too: it is essential that you LIMIT the answers to these questions, otherwise you'll have one of those 'info dump every 5 minutes' stories; and that's another huge barrier to reader engagement. The MC should be allowed to have normal, friendly conversations with others; they shouldn't be absorbing big chunks of worldbuilding all the time.
Make sure you understand the personality and motivations of whoever's going to answer a question from the MC, and factor that into their explanation. Hot tip: most people don't want to/don't know how to give super-detailed explanations of their everyday lives. They also aren't going to share highly personal info with an MC they barely know just because they are curious, or because it's 'sad backstory time'.
Maybe they'll say a little for now, and the smaller details will get filled in later as the MC gets closer to their new friend and learns about the world on their own (and asks follow-up questions). Even though this kind of exposition is usually heavier, it's important for it to feel natural, too.