How does wave refraction occur at a shoreline?

Waves travel slower in shallower water (just like light travels slower in glass than in air), and so the distance between waves gets shorter when the waves enter shallower water. If the waves enter shallower water at an angle with the beach, then the part of the wave closer to the beach slows down and the rest of the wave catches, turning the wave into the beach.

You can see this very clearly at surfing points, where the waves wrap around the land such as at http://www.laurenceplatt.com/wernererhard/timeless.html, or below:

In this image above, you can see that the waves in the deep water are headed to the left. As they enter the shallower water, they are refracted in toward the shore downward to the right. At the far right, very close to shore, the waves get in very shallow water, slow down much more, and turn further to the right, wrapping around the shoreline and come in almost directly to the shore. The tree gets in the way of some of these waves, but you can see it clearly in the wave directly above the tree. The part of the wave that is very close to the point of land slows dramatically, which directs the wave shoreward.