Lately an archive was placed into my mysql database that contains russian letters. The database could not display them correctly. Can there be anything I'm able to do in order to allow diversity of languages on my small website?

you need to have a look at utf8 encoding

are you able to please publish what encoding is beeing utilized by your database, as well as your table? (are you able to publish structure of the db?)

EDIT: To reply to you question inside your comment, fundamental difference is the fact that utf8_general_ci is faster but does not worry about some language specific evaluations. Read more about this within the link I posted above during my publish. Actually it affects behavior of sorting and looking out.

It will matter how does one much like your database some thing, many of these collations are helpful in various conditions. Inside your situation I wouldn't use utf8_bin because it only compares strings using it's binary values.