I have a piece of poster board that I cover my sink with. I have folded the board to rest easy on the faucet, as well as stop any hair from sliding off the paper.
The hair is still dry, so it slides right into the trash when I'm done ( or I put it outside for birdies to make nests out of ).
There are always a few hairs that manage to get on the sink, but I wash them down, as I feel it is less hair than one who shaves everyday would wash down.
I've been using the same piece of poster board for about ten years now.