To determine why salt (NaCl) dissolves in water, we need to understand the interaction between water molecules and the ions in salt.
Step 2: Analyze Each Option
The sodium precipitates, leaving a solution of watery chloride.
This is incorrect because sodium does not precipitate; it dissolves in water.
Polar water molecules surround $\mathrm{Na}^{+}$ and $\mathrm{Cl}^{-}$ ions.
This is correct. Water is a polar molecule, and its positive and negative ends attract the $\mathrm{Na}^{+}$ and $\mathrm{Cl}^{-}$ ions, respectively, causing the salt to dissolve.
Water causes the NaCl crystals to evaporate.
This is incorrect because NaCl does not evaporate; it dissolves.
The hydrogen atoms in water combine with chloride ions to form HCl.
This is incorrect because the hydrogen atoms in water do not combine with chloride ions to form HCl in this context.
Step 3: Select the Correct Answer
Based on the analysis, the correct explanation is that polar water molecules surround $\mathrm{Na}^{+}$ and $\mathrm{Cl}^{-}$ ions.
Final Answer
\[
\boxed{\text{Polar water molecules surround } \mathrm{Na}^{+} \text{ and } \mathrm{Cl}^{-} \text{ ions.}}
\]