How can they separate salt and water to get salt?

We can separate salt from salt water solution using evaporation or simple distillation (shown respectively in the two pictures below). Let me explain how and why:

The solution of salt water is heated so that the water boils and/or evaporates. This is done either by boiling the solution using artificial heat sources or heating naturally by keeping the solution in the sun for a long time, where the water evaporates and escapes and the dissolved salt remains as a residue. This is essentially how salt is separated from salt water solution, and the salt we get remaining is found in a crystal form.

Another method for separation of salt from salt water solution:

Crystallisation:

If the salt water solution is heated and cooled to a very low temperature, the solubility of water decreases and the dissolved salt settles down as crystals, which can be separated using filter paper (this process is known as filtration).

Fun little experiment:

If we put a thick and heavy string in a salt water solution after heating the solution and then cool the solution to a low temperature , and we take the string out (after a few days) we get a beautiful crystal of salt attached with the string.

Why does the crystal form at the string instead of anywhere else?

Ans: The reason is due to something called 'nucleation site'. In simple words, since the string creates a pointy end where the salt crystals could easily form and join with each other to form a even larger crystal easily, that is why the crystal forms at the string much more easily than anywhere else in the solution.

These are some of the ways to separate salt from salt water.