My C++ turn-based game server (which uses database) does not stand against current average amount of clients (players), so I want to expand it to multiple (more then one) amount of computers and databases where all clients still will remain within single game world (servers will must communicate with each other and use multiple databases).
Is there some tutorials/books/common standards which explain how to do it in a best way?
The way you put the database into the picture might be misleading: clustering solutions exist for all of the mostly used RDBMS, so that if you need to support your DB activities with more than one DB node you will just have to check the documentation from your DB vendor.
More complex scenarios are there when it comes to synchronize your non-DB application state that needs to be shared among several servers. There are already a number of questions here that tackle the same problem, like here or here
You might also be interested into some messaging system, I heard good things about ZeroMQ
Hope this helps.