Lay out a sheet of aluminium foil on your working area. This way, when you're finished you barely have to clean up, you just wrap up all the mess into the foil and chuck it away... If you live on your own you can use aluminium foil for plates aswell. or even paper plates. It's great for people who like cooking but hate cleaning.
I put a paper towel down whenever I'm peeling potatoes, carrots, etc. Then I just pick the whole mess up and throw it away. If it's summer, I empty the peelings into a compost bucket and thow the paper away. Aluminum foil seems like overkill!
Lots of great hints here!