I bought a $1 plastic shower curtain liner for Mr. SP's haircuts. Sit him in a chair on top, and just gather it up when done and shake it outside. The liners last for a couple of years before they get torn and need replacing. I keep old towels, and he puts one around his neck to keep the hair off. In the summer, I cut his on the deck, and just sweep it off.
For myself, I save the big plastic envelopes that toilet paper comes in. Cut it open into a sheet, cover the sink area, and cut away. When I'm done, fold it up, throw away. Only a little hair gets on the floor, and it's easy to wipe up.