Probably I won't move anywhere from our capital, but since guys seem to
like roleplaying stuff (or something like that, anyway), and we have
three cities, could you post rules how to change the city you live?

Thank you in advance.

The instructions are listed in this thread: http://forums.civfanatics.com/showthread.php?s=&threadid=11396 and the thread where you change it is here: http://forums.civfanatics.com/showthread.php?s=&threadid=11374

You should read the rules thread closer next time.