The easiest way to determine this is to read the labels on the plants when you buy them. The only hard part is that certain climates are too hot or too cold for certain plants. Usually, the plants you see at your local nursery are a safe bet for your climate, but if you are not sure, just ask. Plants like tomatoes require a lot of sun, whereas impatiens are a shade-loving flower. Something else you may need to know are the two main types of flowers for planting.
Annuals are flowers that have one flowering season.
They usually last only one year and then die. Most of these will last longer than a year if in the right climate, but generally they don't. Perennials are plants that come back every summer. They usually die down in the winter, but come back up in the springtime. These are usually harder to take care of, but well worth it since they last for years.