Another handy tool for clearing the walk is an ice scraper (http://www.neeps.com/seasonal-tools-scrapers.html). It's pretty much essential if there is anything more than a thin sheet of ice. As koshmom states when there is some ice you can use the edge of the snow shovel to break it up. When the ice is 1/4" or more you'll need the ice scraper to break up the ice. Using your garden variety snow shovel on ice like this will not only be very ineffective, but will probably ruin the shovel.

Don't worry, I moved here from Berkeley, CA and I've gotten used to the various complications that snow brings. I would say the number one invaluable item for snow days are good water proof boots. They can be on the pricey side, but having warm dry feet when stomping around in the slushy remnants of a large snow fall will make them worth every penny.