It seems that the radios are still very much WIP. :D
The manual tuning works fine, as do the top row buttons labeled H, 1, 2, etc, if they are properly set in mission editor.
As for the two dials (base selector and group selector), they don't seem to work correctly.
As I understand it, the left dial is associated with the bottom buttons (labeled 0-9) and are used to communicate with air and ground units. There is a kneeboard page with a list of all units, their frequencies and "channels". Those channels are used here. For example, the kneeboard gives 3-1, you turn the dial to 3 (have to guess where that is, since the window doesn't show correctly) and press button 1. I've manage to get it to work, at least I heard other planes talk.
The right dial is used for ATC comms, in conjunction with the buttons above it (A/G, B...) and in a same manner as above. The kneeboard provides a channel e.g. 4-A for Krymsk VHF, you turn the right dial to 4, and press button A. But the dial doesn't turn and I couldn't get it to work.
edit: there are some other issues with the radios, reported here.