see the heading (translated from my German ID) >>> input method options, check this box and use the integrated input for non-Latin text. This ensures that languages such as Cyrillic, etc that are not based on the Latin alphabet, can be used in InDesign anyway. And note: The operating system of your computer must support this language systems. Otherwise it does not work.
Another possibilty would be that you use WORD (or similar) to build your text and put it (copy and paste) into your ID.
On the other hand you could use fonts like Myriad Pro oder Minion Pro and integrate them into your WIN or MAC, so that ID can find them.
Adobe can provide you Russian fonts too, please have a look at
I've checked that "input for non-Latin text" box and nothing changed.
The problem is that if I create a .indd document out of nothing there is no problem with russian font.
But when I try to translate already made file this squares begin to show up.
P.S. I'm using a PC with Win 7 OS and ID CS 5.5
it did not leave me in peace , but I fear I don't understand in the right way. The only thing I can offer you are links to russian fonts. They say you can unse them in ID, no matter how you use them. Here the links:
All the best!
Check the paragraph style when you type Russian. Do you see an override (the +sign on it). If that's the case clear the override and see it that works.