What do you mean "what kind of cooling?". The nitrogen is kept under high pressure and at low temperature. When liquid nitrogen is released from the tank (by a tube at the bottom), it starts boiling, the boiling temperature is 77K (ish). As it doesn't all boil off instantly the effect of some of it evaporating takes heat out of the liquid.
Rapid expansion of a gas needs work against the air pressure, thus the heat is taken from either the liquid nitrogen or from surrounding heat sources. The reason for the ice build up on tanks and dewars is due to the expansion of the gas and cooling effect of a cold liquid on the pipes which in this case is sufficient to condense water from the air.
If you want a more visual representation, try turning a lighter gas refil can upside down and squirting the resulting liquid into something plastic. Despite the can being at room temp, the liquid formed is at the boiling point of the gas which is about -30, The gas expands, cooling the liquid until an equilibrium is established. If you're really keen look up the zeroth and first law of thermodynamics and derive the phase change equations from there.