We have reached temperature as low as 0.00000001K in the lab and as high as millions of degrees in a nuclear bomb.
We achieve such low temperatures by using different techniques. Laser cooling is one of them. In laser cooling, where we fire photons in a certain direction which are accepted and reemitted by atoms in such a way that they retain a component of velocity in a certain direction only. This happens for many atoms and ultimately we have an orderly motion of atoms which don't contribute for temperature calculations (temperature is a measure of unorderly motion of particles).
Magnetic Refrigeration is another popular method used to produce liquid nitrogen and helium.
We can achieve very high temperatures using laser heating. The idea of using lasers to increase the temperature to millions of degrees is already being used in fusion reactors (experimental reactors). The idea is to fire concentrated laser beams at a point to increase the temperature. The matter exists in the plasma state in such high temperatures and we make use of strong magnetic fields to confine the plasma to a region.