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.
"You know nothing, Sergeant Schultz"