The key: When you hit the grocery store, just buy a little bit more than what you actually need. Keep a running inventory of what you've got on hand. Don't panic.
Rice, beans, grain: Buy in bulk. Think 50-pound bags. Lift them in your basement for (creepy) exercise in your spare time.
Sugar, salt, spices: These help in a number of ways, including making your end-of-the-world menu actually taste good.
Peanut butter, assorted canned goods: The longer the shelf life, the further ahead you'll be looking. Begin with stock for three days, then go from there. And remember: creamy over chunky, always.
Bottled water (or a water filtration system): Water is priority numero uno in times of distress. One gallon per person per day is a good ratio. Alternatively, know how to build a fire so you can boil water collected outside. Ignore Waterworld jokes.
First Aid kit: Get as expansive as you're comfortable with this one. Learn a thing or two about amateur surgery before the time comes when you're forced to perform.
Light source(s): We all learned this during Superstorm Sandy. Flashlights, candles, leftover July Fourth sparklers: Have 'em handy - and stash extra batteries away, too.
Map: Get to know your local geography firsthand, particularly the great outdoors. This is different than the geography of your most recent West 6th Street bar crawl. For many reasons, don't rely on the latest iOS Maps app.
Personal items: Be cognizant of all personal staples (glasses, prescription meds, porn stash) that you'll need to get by.
Further reading: Local preppers recommended Zion Prepper's "The Prepper's Handbook: A Guide to Surviving on Your Own." You can also dig into the Internet's vast reserves of information. The American Prepper Network's forums are a good (and/or entertaining) place to start.