I'm sure it's more complex than I'm making it out to be, but each gas in the air has its own freezing/melting boiling/condensation/sublimation points, so I'd imagine you could just kind of take advantage of that

Basically just cool it down to x temperature at y pressure, and all of the carbon dioxide should be solid, the oxygen a liquid and the nitrogen still a gas, and they've all sort of separated themselves out. Fish out the dry ice, siphon off the oxygen, and you're left with nitrogen.

Might need to do a couple more rounds of that on each of those to account for other gases in the mix depending on how pure you need it to be, but in theory I imagine it could be that simple (again in practice I'm sure there's probably a lot of details I'm missing)