Temperatures down to a few millikelvins can be reached using dilution refrigerators. Below this temperature, nuclear demagnetization is the most common method used in ultralow temperature laboratories. Temperatures as low as 0.5 mK can be easily obtained. Cooling samples below about 100 µK is feasible, but extremely difficult, and highly dependent on the type of material. Superfluid 3He, for instance, has been cooled down to about 80 µK in Lancaster and in Grenoble.
The principles of nuclear demagnetization are described in section textbooks. Specialized articles describing modern demagnetization systems can be found here.