Practice typing in Russian with the game Хамелеон. You can even enter your own text to type by clicking Введите свой текст.
Keybr is an excellent online typing tutor that will even teach you how to type in Russian. Navigate to keybr, click Language/Layout, and choose Русский. The keyboard layout is the Russian standard. You can change the text source (источник текста) and the level (уровень) by clicking on Tutorial, and monitor your progress by viewing the graph (график). Try changing the text source to song lyrics, Wikipedia articles, blog entries, news stories, or literary texts to make things more interesting.