The molecules in any body of substance will have a certain range of energies... For example, in a body of water at 20C the average energy of all the molecules is that corresponding to a temperature of 20C... However some molecules will momentarily gain an energy in excess of that corresponding to 100C from a collision with another molecule. If this molecule is near the surface, it is likely to break free into the vapour state. When one considers that an average molecule will have 10^10 collisions per second it doesn't take long for the odds of energies  (thats 1 followed by 10 zeros) equivalent to 100C occuring to build up. As it is in a more or less open system, this process of energy transfer between water molecules will continue until all the water has evaporated.