The hydrophobic effect is entropically driven - hydrophobic (non-polar) atoms like to pack away from the water solvent. Hydrophobic atoms exposed to solvent cause ordering of the surrounding solvent; this order is entropically unfavourable.
The practical effect of this in proteins is that hydrophobic sidechains (such as valine, leucine, isoleucine, etc.) tend to pack on the inside of a protein, while hydrophilic sidechains (such as glutamine, asparagine, serine, etc.) tend to be on the outside of a protein.
View this structure (lysozyme, 7lyz) using PyMOL. We will now colour all the hydrophilic residues in red and the hydrophobic residues in blue.
You can now see the surface of the protein and you will see that, while there certainly are a number of exposed blue (hydrophobic) sidechains, most of the surface sidechains are red (hydrophilic).