Let's say that a certain mammal is writing a historical fiction, based in a society that doesn't really exist anymore. Said mammal can't write his story without dialogue, but he doesn't really know how people of the time would have spoken. Does he just write as he normally would, or come up with some slang expressions or something similar?

Depends. He probably would just write about it in the language he knows, so as not to confuse the reader. If he KNOWS any of the slang at the time, he might use that.

You might want to check out a few of the more diplomatic passages in Herodotus' Historiae (I'd recommend the passages about Gelon, Athens/Sparta and similar). He aims at what for his time is relatively reliable information (hearsay, self observation and dialogue re-construction) and he provides every scrap of information he can get his hands on.

But the point is, most of the dialogue he uses is dialogue he has had to reconstruct. There might be documents detailing what was said during official diplomatic missions, but not of what is said outside of it.

Writers should always research before they write... even fantasy fiction requires some research (even though for most the writer makes that up too)

When it concerns historical fiction and spoken dialogue and discourse, the writer should look into areas such as slang, the internet can always help, or if possible museums always employ historians. Or if the writer was brave contact the linguistics department of a local university, they will know of plenty of research based on past or 'forgotten' communication systems.

I woulnd't touch it. Just use modern English. Nobody knows how people spoke in the past. The only thing we know something about is written language and even then knowledge is scarce.
Besides that old languages have many different dialects. 
So it wouldn't be correct and personally I find it annoying when writers do that.
(Also depends on what society you're talking about ofcourse.)
just my humble opinion though :p

The society I'm looking at is late Edo Dynasty under the Tokugawa shogunate in Japan, slightly before 1800. But I probably won't try to replicate the way the spoke. The notion hit me that the meaning what they said would be lost in translation anyway.

*keeps her hands off of Japanese* . Yeah also because of the cultural differences... Translating never does just to the original language and when the language itself isn't spoken anymore it would be even a bigger problem.

The thought I had was about how greatly changed the English language is, even since a century ago. I mean... hm... *gives an example*

When I tried to struggle my way through War of the Worlds when I was in junior high school, I came upon the perfect example phrase. I don't remember the words verbatim, but it went something like this...

"he came down the stairs, ejaculating"

... which in context meant 'hesitating'. I'm sure that most languages have experienced similar changes, especially over the course of two centuries.

o.O That would be ..weird :D

Yeah I know. Some languages more than other. French for exemple has been pretty much the same over the past 500 years.

Also this century has created lots of new terminology