In Russia it is mostly Old Church Slavonic or Russian. In other countries it is the national language for example in USA English is the language of choice but in many areas where the population is largely Russian than they will use Russian and Old Church Slavonic or a combination of several of them.

Milver

Old Church Slavonic

~Ates

Old Slavonic.

Ivan the Great primarily spoke Old Church Slavonic, which was the liturgical language of the Russian Orthodox Church. He may have also spoken Russian, as well as Tatar due to interactions with the Tatar-Mongol Khanate to the south.