There are many companies nowadays, but to tell the truth the only company for foreigners I know for a good reputation is Intourist - the one from the USSR times. Here is the link to the Intourist site you can consult for their prices and programs. Intourist - Tours in Russia. Hotels in Russia, visa, transfers, excursions.
However, I should say that their program is too short. (((((( And in fact can not be called Golden Ring at all.
I found also couple of other companies with relevant info, but have no idea if they are as good as they say:
Tours and Travel to Russia | Go To Russia | Russian Travel | Express To Russia
Fixed departure group tours
The Golden Ring Russia: Tours and Cruises
Golden Ring
BR
Maria