The story I'm writing has a lot of different races and I've been thinking about how they would all communicate. I'd imagine they'd all have different languages (and probably different languages within the same species), but I'd imagine they could learn to understand each other. The one question I haven't figured out is if such races could even speak a human language; would their throats and vocal cords allow them to form the correct sounds? Many of my races evolved from chalicotheres (ancient, knuckle-walking ungulates), while others are descended from ancient crocodile relatives. Could a race like these evolve to be capable of human speech? What kind of biology would allow for such speech?
The simplest answer that can be given to this is that at a minimum, alien species will need some form of vocal chords that vibrate over an airflow to generate the sound, and some form of cavity past those cords that can be dynamically shaped to form the sounds out of those vibrations that we can interpret as speech. In humans, that is the throat, mouth and tongue, all combined to dynamically shape those vibrations into a large array of different sounds.
But, two points; the first is that we don't only communicate via speech, and the second is that your aliens could converse via a massive and diverse range of potential information exchange protocols.
Not all humans are born with vocal cords or working ears; in those cases, they use things like sign language and writing, both of which only require working limbs or fingers. If your aliens don't have a working set of vocal cords, but have fingers, in theory they could communicate to humans that way.
Of course, The vocal cord structure doesn't even have to be attached to the lungs; in some aliens, particularly those who are largely vegetarian grazers, they may have a flatulence driven sound generation model. But, they could just as easily communicate by pheremones, ear movements, telepathy, interpretive dance... almost anything you can imagine. Some of these could be translated directly into a form that we could understand; some not so much.
It is said that more than 80% of human communication is non-verbal in nature so while the original answer above is an accurate answer to this question, it is important to note that there are many other forms of communication that your aliens may use that we can adapt to or they can adapt to something we can readily understand. It doesn't necessarily have to be speech.
You are writing. Have them write too.
You are writing a story. Having your aliens communicate with written messages lets you leverage your own written format. Instead of you writing "Grok started grunting 'bad'" you can write that Grok writes on his board BAD BAD TAT BAD! then taps the words with his finger so hard he breaks the board. He has several spare boards; not the first time.
Each character can write in its own font with its own patois when they have dialogue. You will eventually not need to say who is speaking because it will be clear from the font. It will be lots of fun.
Plus writing is a perfectly legit way to communicate for all sorts of people.
A study was carried out teaching a chimpanzee sign language. She was able to describe new items. Like a thermos was "hot" +"bottle".
Even able to pass the sign language to other chimps!!!
So there you have it. Human <-> chimp inter species communication without sound. Using different hand structure yet it was possible.