Stan DeFreitas, Mr. Greenthumb, explains some of the items that you might need to get started with your first vegetable garden.
Stan says that you might want to start out with a few garden tools, and a good watering can.
Improving the soil is one of the most important things that you can do if you want to have a successful garden. Mr. Greenthumb recommends adding compost, peat, and perlite (or vermiculite!) to make the soil nice and loose and fertile. You can substitute coco husks, also called coir, for peat moss.
A raised bed garden is a good way to build up your own high quality soil on top of the native soil.
Starter plants are often easier to work with than seeds for beginning gardeners. But seeds are very cheap!