Shinigami are totally different from humans, so how do they speak to each other? How can Ryusaki and Ryuk speak the same language?
When a person who takes the Death Note when it lands on the earth becomes it's owner and the Shinigami is forced to remain by the Owner until they relinquish the Death Note or die.
One reason would be that the Death Note would understand any language a person's name is written in provided the rules to the Death Note's usage is for-filled, that would mean the Death Note is capable of understanding all languages, evidence of this is with making the eye deal allows one to reads people's names by looking at them so the names have to be in the language that the person can read, because the eye deal can only be made with a Death Note Owner and Shinigami originally owned a death note Shinigami may also be able to understand all languages as well.
Another reason could be is that Ryuk wrote the rules on his second Death Note so that anyone could pick it up and understand how it works, he even says to light he "chose the most popular language", this could mean that Shinigami know "the most popular language" (English or Japanese depending on which version of the anime you are watching)
Finally, only those who have touched the Death Note can see and hear the Shinigami who belongs to that Death Note, so to the person hearing a Shinigami they may be hearing them speak in their minds and the Death Note is translating it for them and what they see is the Shinigami talking, kinda like how the TARDIS in Dr Who translates since The Doctors companions would see other languages spoken as English (quite sure the only time this is questioned is when a companion finds it confusing that another race knows English and not from not bad lip syncing of another race speaking English but mouth movements not matching)
i should point out this is regards only to Death Note as your question asks and not to Shinigami, if you was to ask about Shinigami in general then the best answer would be "their gods, how they work is beyond mortal understanding"
Although I'm unaware of any canon quote in Death Note that explains the ability of supernatural beings to speak to humans, there is a rich cultural tradition around the Shinigami or "Death Spirits" in Japanese classical literature and folk tradition going back to the 1600's where they are referred to as Kami. More recently they are found in post-war Manga such as GeGeGe no Kitarou (dating back to 1959) and even more recently in modern anime such as Full Moon o Sagashite, Bleach, Yami no Matsuei, Black Butler, Soul Eater and Death Note.
The Shinigami seems to have evolved over the past few hundred years from an demiurge (or minor god) capable of influencing actions from the spirit world to becoming an full-on evil spirit akin to a demon capable of possessing humans and controlling their speech and actions which would necessitate them speaking Japanese.
Out of universe, it simply makes sense to have main characters be able to speak to each other, even if there's no sensible reason why they should be able to.
All I can think of is that Ryuk can speak many languages. I couldn't find it directly said, but I found some pictures that agree with what I said.
Picture 1 is said by Ryuk talking about why the deathnote is in english.
Picture 2 is said by a victim talking about the deathnote.
He deliberately writes the instructions inside the front cover of the Death Note (in English, which he assumed to be the most popular language in the Human World) so people would understand its purpose.
From the canon material I think it can be seen that Ryuk knows other languages allowing him to speak to other people, him having a native shingami tongue is debatable, though.
Also, in the manga Ryuk mentioned something about him and his first victim having a "bond" that allowed only the victim to see him, so this might be why they can speak to each other..
I call the person he gave the deathnote to his victim, as I don't know what else to call them.
Another note is that the message regarding this might change depending on what language you read it in. I read it in English and tried to read it in in the native tongue(but my skill sucks), so since this is a translation if I am not mistaken things could be lost or altered to change the original meaning.
Also from the fact they often get apples and other things from the human world, it would make since for them to be able to read labels and if possible talk to humans.
Me and this guy I read it with remember somewhere in the manga that Ryuk said something about being able to speak other languages. Which given these 3 theories could or could not make sense:
Theory 1- Ryuk can only speak one or 2 languages, because he is native to the area around Japan.
Theory 2- Ryuk can speak numerous languages as he possibly travels and to travel he has to be able to speak to his victims.
Theory 3- Ryuk can only speak 2 languages or so, because he doesn't really speak to a lot of humans and the ones he gives the Deathnote to he gets a "bond" which allows them to speak to each other.
- The third theory is not really a theory, but more like a extrapolation(if I am not mistaken the word) as it is proved in the manga that Ryuk can speak at least 2 languages and the victim "bond"(or whatever you want to call it) is in the manga as well.
Combine the factors
- Shinigami can observe the human world from their world
- Shinigami are ancient
- Now and then, Shinigami need to pick a human to kill to continue living
So we have that for millennia, Shinigami have been observing humans from time to time (because they need to). It's just natural that they'll understand human language over time.
This is an incredibly common trope in science fiction, as well as other genres. Here's a TV Tropes link on it. Warning: coarse language on the other side of that link.