For me, 'seven sixty-two by thirty-nine'. I've also heard it called 'thirty Russian' (.30 Russian), but, IMO, this is not a good description as 7.62 X 54R could also be called .30 Russian.
I think what you're calling it is correct and would be understood by most gun enthusiasts. It's interesting that the employees at the shops near you don't know what you are saying. What do they call the cartridge? I'm guessing something like, "the round the AK fires" or "the AK round".