Peeling potatoes is a dirty job and if you're peeling a whole bunch like I do for this Easy Scalloped Potatoes recipe [1] then they also can start to go brown before you're even done peeling!
For easy clean-up and to prevent your kitchen sink or counter from becoming a slimy potato peel mess, simply place a plastic grocery bag into your sink and peel potatoes directly into the plastic bag. When you're done peeling just toss the bag away or take out to the compost or green bin and empty.
To prevent your now-peeled potatoes from browning before you're ready fill your other sink with just enough water to cover the peeled potatoes and add 1 tbsp of white vinegar. When you're done peeling each potato just toss into the vinegar water and they'll stay white until you're ready to use them.
PS: This also works if you're boiling a pot of potatoes — just add a tbsp. of white vinegar to the water before boiling and cook as usual.