Absolute zero is an unreachable ideal; there is even a Law that says you can never get all the way there, sort of like the speed of light. But scientists have gotten down to within a few millionths of a degree of absolute zero, using refrigerators the size of houses. The big problem is exactly what you imagined: measuring such low temperatures once you get there! You certainly can't stick any conventional type of thermometer into it -- in fact even unconventional thermometers tend to introduce some sort of jiggling that raises the temperature.
One trick is to look at some external effect caused by "ordering" of weakly-coupled systems like nuclear spins -- as T approaches zero, all the spins start to line up and then their (small) magnetic fields can be seen from outside the refrigerator. This works, but it takes a lot of interpretation. It may seem vaguely dissatisfying to have such an esoteric way of defining the temperature of a system, but when you look at what temperature IS in the first place, things get even weirder. If you're interested, have a look at my Web site on this topic, http://musr.physics.ubc.ca/~jess/hr/skept/Therm/. You may have been told that, "At absolute zero, all motion ceases." This is wrong. Classically, yes, but in the real (quantum mechanical) world, all objects find their lowest energy states and in those states they are not at rest but are executing "zero-point motion" -- so even at absolute zero all the atoms in a solid are jiggling like crazy; they just can't jiggle any LESS. Drive your Physics teacher crazy with this!