Russian Typing Manual
Typing in Cyrillic is simple once the IME (Input Method Editor) is installed. Select the program you want to type in and then select the Russian IME (keyboard), by clicking on RU Russian or Russian - Phonetic. You can see this being done in the pictures.
Windows Language Bar
Macintosh Language Bar
If you follow the directions you will install the Russian - Phonetic keyboard on a Mac, and the Russian keyboard in Windows. You can see a layout for those keyboards below. You can also see the keyboard you are using by enabling the on-screen keyboard. As you can see, the keyboards on Mac and Windows are quite different. This is the difference between a phonetic keyboard, and one found in Russia itself. You can search for alternate keyboards as well. To see the layout of those keyboards use the on-screen keyboard.