In the distillation column, the liquid air boils up thru a bubble plate of more liquid air. The bubbles rise thru the liquid air and some of the oxygen in the bubble boils out more than the nitrogen. It goes thru a whole series of plates until the oxygen exits the top at about 99% oxygen. The more plates (which equates to multiple distillations). Oxygen boils at less temp then nitrogen so it gets to the top quicker. Since more oxygen boils out of the trays of liquid air the trays become more nitrogen percentage the closer you get to top. And the same thing with nitrogen, the more trays you have the purer it is by the time you get to the top.
The clade process is much better from an energy standpoint. Here you take compressed air but instead of going thru a throttle valve, you direct the air against a turbine or piston which takes work out of the gas. The temperature decrease is much more dramatic. Where in the Linde system it takes 1 atm pressure to drop the temperature 1/4C, the Claude expansion drops the temperature by 10C. This means with only 5 atm (74 psi) you can drop the temperature by 50C.
There is a lot to it, especially the factors of heat exchangers and clearing out the H2O and CO2 from the air first. Georges Claude made his heat exchanger out of a gutter pipe with 10 copper pipes in the middle of it. He used a little piston motor with a leather ring to compress his air and also for the expansion ( Expansion engines get so cold you need motors without lubrication since the cold will freeze the lube oil) Read that book if you can find it. He gives the exact method he used to make liquid O2 and N2 and all the trial and errors he went thru to make it. It took him about 5 years just to make that first drop.
If you can't find Claudes book, there is one made in the 1960's which is a Mechanical engineering series book from McGraw Hill publishers. It was by author, Barron, and titled "Cryogenic Systems".
It isn't near as good as Claude's book, who writes more like Mark Twain and makes science fun to read. This book by Barron seems more like todays textbooks where the authors are more worried about impressing their colleagues then teaching people.