How does one use a paper that's not written in a language that he can read? For instance, if a paper is written in Russian, and a researcher wants to use this work and cite it, does he have to learn Russian?

What's the typical practice?

Does he try and use translation tools such as Google translate?

Pay a professional translator?

Or, blindly accept the results and blindly cite the paper and move on? 

(The last option is problematic, if one wants to write a self-contained piece of work, using the results and proof from the original work.)
There is no general answer to your general question. It depends on a paper.

Do you have to cite it? We know that a2+b2=c2 and we don't cite Pythagoras manuscript on it. We don't cite the basic results we use.

Do you have to read it first? You probably don't read Disquisitiones Arithmeticae in Latin to quote some of Gauss results, and you don't read Théorie des mécanismes connus sous le nom de parallélogrammes to check if Chebyshev polynomials are correct.

So, if a result is already well-established, many people have seen it, checked it and built their work on it - you don't have to read the original paper, if you don't want to. If you really want to understand how some details were presented originally (for methodological or historical purposes), you can check if some colleagues in your University can read this language. If they don't, you can hire a translator, but it is not easy to find one who can also read understand math arguments.