How can I stop puddles of water forming on the shelves of my new refrigerator?
Simply saying what MaxW said already: Make sure the fridge doors seal. When freezer doors don't seal you get that frost we all loved as kids but when the fridge door does not seal, you get little puddles forming around/under all your pots and containers. If this is the case, you can use the following suggestion from popularmechanics.com:

"This can be the result of a leaking door gasket. The gasket allows the cold air to constantly seep out, making the refrigerator run overtime and produce extra chill in the freezer. Check the gasket by placing a high-power flashlight or emergency battery-powered light unit in the freezer with the beam pointed at the door. Turn the light off in the kitchen and check around the perimeter of the door. If there is any light leakage, you'll need to replace the gasket, which can be purchased directly from the manufacturer or from large-appliance retailers."