The easiest way to actually determine the temperature of liquid nitrogen is with a constant pressure gas thermometer (we’ll use CPGT for an abbreviation). This is also a method useful for determining absolute zero (see other articles regarding this temperature.
A CPGT is a narrow tube of uniform diameter closed at one end with a close fitting, gas tight piston on the other. One side of the piston is exposed to the atmosphere. This utilizes atmospheric pressure to keep the pressure in the tube basically constant. The tube is filled with a simple gas, typically helium due to its low boiling point. You can calibrate this thermometer with a simple two point scale using the boiling point of water (100 celsius) and a water/ice mixture (0 celsius). At each of the temperatures the helium gas in the tube will occupy a different volume. As long as you do not approach the boiling point of helium too closely, the contained gas can be treated as ideal. This means the gas molecules (atoms in this case) do not interact (except when they collide) and have essentially zero volume compared to the volume of the container. Under these conditions, if the pressure is constant and the number of atoms is constant, the volume of the gas is linear with respect to temperature. You take your two points and mark where the piston is from the bottom of the tube. Since the tube has a uniform diameter, volume is linear with respect to length and, hence, the length of the tube the gas occupies is linear with the temperature. You put the calibrated CPGT in the liquid nitrogen and measure the length of your piston from the bottom of the tube. The length between the first two marks corresponds to 100 degrees celsius difference. A simple ratio is then sufficient to find the temperature of the liquid.
If atmospheric pressure is the sea-level value (a little less than 15 psi or slightly more than 101 kPa) then the temperature of liquid nitrogen is about 77 K. If the pressure is reduced, the temperature will be reduced due to the boiling. Reducing the pressure sufficiently will result in the nitrogen freezing. This occurs when the pressure reduced temperature is about 66 K. Should this happen in a well-insulated container, you may have to wait several days for the solid nitrogen to melt, as it has a very large latent heat of fusion.