How are things cooled from very cold to near 0K?

I mean from like subzero (~250K) down to within 1-2K when laser cooling and fancy physics tools are used - for commercial uses like liquid nitrogen, dry ice etc.

Liquid nitrogen is the quick ‘n’ easy way to cool things down to 77 K. It’s cheap (cheaper than soda or beer). More important, it’s not dangerous – unlike liquid oxygen, it won’t support flame, and it won’t burn like hydrogen. 3/4 of the surrounding air is already nitrogen anyway. Unless you displace an awful lot of ambient air, you won’t get hurt. And 77 K is good enough for a lot of low temperature detectors and electronics, the newer “High Tc” superconductors, and the crystals used for color center lasers.

If you want to go lower, you can use liquid helium. In prinxciple, you could use hydrogen, but it’s dangerous. Helium will get you to 4.2 K, but you have to use a lot of it, because it has very little heat capacity. The usual practice is to cool to 77 K with liquid nitrogen, then use helium the rest of the way. If you don’t have to get too cold and have a small sample, you can use a helium refrigerator to get to about 14 K or so, and you get to re-use the helium! The easiest way by far to get to that temperature.

To go below 4.2 K you have to start playing tricks. You can pump on the helium to get a little lower. A helium dilution refrigerator takes advantage of the difference in behavior of different helium isotopes to get you down a couple of degrees further.

Beyond that point yuou need even slicker tricks. Someone once said that it takes as much effort to halve the distance between your temperature and absolute zero as the previous step did. You can line up magnetic moments in a strong magnetic field at low T, then remove the field, and the increase in randomness buys you some temperature. You can use other such methods that take you from ordered to random states as well. Low enough in a gaseous state you can use laser cooling to strip momentum from your atoms or molecules.

some interesting things in Wikipedia:

I think the Gifford-McMahon cooler is the most common method of achieving cryogenic temperature (20K or lower). It’s a closed-cycle refrigerator that uses helium as a working fluid. Helium is compressed, cooled to room temperature or lower (e.g. by a radiator or chilled water), then goes to an expansion chamber and allowed to expand rapidly. Expanding gas results in lowered temperature (Joule-Thomson effect).

I don’t have a very comprehensive understanding of physics, but this seems like a cop-out to me. How do you make something cold? Well, liquid nitrogen is cold, so use that. Okay, but how did the nitrogen get so cold that it became a liquid? If you just found it somewhere, already in liquid form, (like the way we can find solid ice in areas with below-freezing temperatures) then what’s keeping it cold there?

It’s chilled in a fridge using fundamentally the same principles as a normal kitchen refrdigerator but with more exotic coolants.