Finding your plant hardiness zone couldn't be easier (sort of). The Arbor Day Foundation has a great feature on their website where you put in your zip code and you can find out your plant hardiness zone. The Burpee company also has a page with a map and a description of zones 3-10, with their approximate last frost dates.
That said, you can also have micro climates in different parts of your yard, balcony, patio or deck, that defy the zone suggestions. For example, on one side of my house, I'm a different zone than on the other side because one side is much more protected and warm than the other side. It is only through observation, experimentation and time that you will know if your USDA zone is really true to the temperatures your plants will experience.
Knowing your plant hardiness zone is particularly important if you are growing perennials, trees or shrubs in your garden pots. If you live in a cold zone, you'll want to make sure your plants are rated for two zones colder than your area, because the roots of container plants get colder in pots than if they were in the ground.