How do you separate it?

Fractional distillation of liquid air I believe (like separating petrol and diesel).

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)

There are filters that you just need a little compression to get close to pure nitrogen out of, then a lot of cooling to liquify it.

Generally it’s made by first filtering out other gasses (there are materials that will pass nitrogen but block oxygen), and then you just get it super cold with a cryocompressor (uses helium as a refrigerant) to liquify it.

you can't turn a gas into liquid by compression alone if temperature is above critical point, you also need to cool it down. separation is done by fractional distillation, but the reason it's done is mostly about oxygen (medical and steelmaking among some other uses). for nitrogen it's somewhere about -150C. first air is stripped of water and carbon dioxide, then it's turned into a liquid, then it's separated into oxygen, nitrogen and argon, and some large specialized plants also separate xenon, krypton and neon

if you don't actually care for it being a liquid, there's another method called pressure swing adsorption that separates gases based on how tightly do they bind to porous surfaces under pressure. this is how medical oxygen concentrators work

making liquid nitrogen is pretty efficient these days, as in not much more energy is used than is actually needed