First, there's the standard Russian keyboard layout ЙЦУКЕН (JCUKEN). You can usually activate it in the settings of your device. In that case, you will have a hotkey combination like SHIFT+ALT that will allow you to switch between your standard US layout and the Russian one. Remembering this layout will take some time. The especially difficult part is that, since Russian has more letters in its alphabet than English, some letters end up in strange places on the keyboard.

To make it easier, you can activate the "on-screen keyboard." It will look like this: