Alien languages, we can assume, will function more or less like human ones. They may have different sets of sounds, different grammatical rules, but they all have the same purpose: to communicate. It’s really what they communicate about that’s where worldbuilding meets language-building.
Personally, I’m not a big fan of the theories stating that a language influences its speakers’ thoughts to the point where they are unable to understand or even imagine those things the language can’t say. If that were strictly true, loanwords would be all but impossible. No, the brain is more complex than that. We can make new words (or borrow existing ones) for new ideas. That’s kinda the whole point of derivation.
But it’s aliens
Now, when you throw aliens into the mix, things change. Their brains likely won’t work the same way as ours. They’ll still be associative, probably, but the associations they make will be far removed from what we know. So it’s entirely possible that they will have words that literally have no translation into human tongues, and vice versa. Different environments, different evolution, different biology will all play a role in this, so it’s up to you to know how your aliens “work”. Only then can you decide what words they’ll have.
Clearly, any word for a terrestrial species won’t have a direct translation, unless you have some serious backstory going on. (On the other hand, for a fantasy race, such as elves, it’s entirely acceptable and expected that they’ll know the same plants and animals humans do.) But take a step back. Look at the wider world.
Those things not affected by the differing biology of aliens can be relatable. It’s not hard to see that they’d have words for astronomical phenomena (sun, moon, planets, etc., depending on their homeworld’s specifics), though they’ll probably have different cultural connotations. An Earthlike planet, similarly, will have weather—weather much like Earth’s—so there will be an array of weather terms: rain, snow, cloud, wind, and so on. Other things that aren’t tied to the biosphere can also cross this divide: chemical elements, fire, water, mountains, oceans. Essentially anything in the “non-living” sciences works here.
It’s with biology and its subgenres that the real fun begins. Your aliens will have their own names for their own animals, plants, body parts, occupations, and cultural paraphernalia, among other things. Some of these can be related to our own: if an alien calls the part of its body it talks out of a “glorb”, it’s a safe bet you can translate that as “mouth”. Others…not so much. Imagine, for instance, an alien race capable of seeing into the infrared. Those guys will have a whole host of color words that make no sense to us at all. A species of eight-legged bug people might have special names for those extra limbs, but we’d refer to them all as “legs”. If they’re lucky, we might divide them into “forelegs” and “hindlegs”, but we’re not going to recognize the nuances.
Really, designing an alien conlang’s lexicon is more an exercise in defining its culture than anything. In that regard, yes, language influences thought. But from a designer’s perspective, let’s look at it the other way around. How do your aliens think? What makes them special, compared to the humans of Earth? Let those questions, among others, be your guide. Find the ways aliens differ, because that’s where their lexicon will be, well, alien.
First contact
It is easy to go too far here, however. Much of the language will be somewhat compatible with a terrestrial tongue. It may not be exact, but it won’t be too much worse than translating between two wildly different natural languages. Our six thousand get up to some pretty crazy stuff already, especially in the vocabulary department. Even if we don’t have a perfect translation, we’ll figure something out.
If you’re making an alien conlang for a story, it’s almost a certainty that you’ll have some kind of “first contact” situation. There, if the aliens are at all like us, they’ll know to keep things simple. Diplomatically speaking, it’s best to adjust your level of speech to that of your listener, particularly when the wrong word could spark an interstellar war or something of that sort. So you don’t have to go overboard on the “alien words for alien things” bit. Sprinkle in a few words here and there to make them feel otherworldly—names for weapons or lesser alien species are a good choice for this—and call it a day. Everything else will have a reasonable interpretation in English or your natural language of choice.
However you go about it, the lexicon is a great place to really drive home the otherness of an alien race. Most readers and viewers won’t bother figuring out the finer points of grammar or making sense of the strange sounds emanating from alien mouths. The words, by contrast, are right there. They’re front and center, most notably when an alien speaker drops one into casual conversation, like they do in every sci-fi movie or TV show ever. In some cases, that might be your only opportunity to flesh out a culture or world that wouldn’t otherwise get screen time, so take advantage of it.