How do salt crystals evaporate in water? Salt dissolves in water but when water has evaporated it is still there. What has happened 
to the salt in the water and why is it still there when water has evaporated?
 A: Water is a strong solvent. That is one of the reasons that it is so essential to life on this planet.
It is a good solvent due to it's polarity. The $\mathrm{H_2O}$ molecule is asymmetric with the two hydrogen atoms twisted towards one side making that side "more positive", and the oxygen atom towards the other, making that end "more negative". This appearance is called a dipole and has a dipole moment. See this answer on Chemistry SE for some illustrations.
Dissolving in water
Simply said, when a solid salt crystal is submerged and surrounded by water molecules, each water molecule rotates to turn one "charged end" towards the surface atoms of the salt. Those atoms now feel two forces: one holding them in (attraction from their neighbouring salt ions (cations are attracted by anions and vice versa)) and one pulling outwards (the accumulated water molecule "pull").
The stronger force wins. And that is that of the water. A similar phenomenon happens when metals are submerged into acids - water is not a strong enough solvent for metal ions to be ripped free, but (some) acids are (depending on the metal).
This is fundamentally how dissolution of solids into fluids work. 
Solidifying during water evaporation
There are now dissolved salt ions flowing around in the water (standard kitchen salt $\mathrm{NaCl}$ would dissolve into sodium and chlorine ions, $\mathrm{Na^+}$ and $\mathrm{Cl^{^-}}$).
Raising the temperature will eventually cause the water molecules to separate into a vapour. They evaporate because the van der Waals forces that hold water molecules together are relatively weak and not strong overcome the violent thermal vibration. Salt ions do not evaporate, though. They are heavier and bind differently to the water molecules.
As you may know, only a certain amount of salt is soluble into a certain amount of water. That is the solubility. So, as water evaporates, we get closer and closer to the solubility limit. When the limit is reached there is "not enough water molecules" left to keep up the forces that separate the salt ions. Then the salt ions feel a stronger attraction to each other, and so they recombine. 
Eventually, all water has evaporated away and the salt is left behind, now as an again solid substance (many tiny crystals).
