Here is a good "virtual" keyboard...
http://www.russianlessons.net/software/keyboard.php
I know there may be others, but this seems to be a good "virtual" keyboard to allow you to type Russian letters. You can change the language on the bottom left of the keyboard, type what you need, then just highlight and cut/paste onto another webpage. (press control c to cut, then control v to paste). It seems rather awkward and slow, even to me, but it gets the job done!