You can start your seeds indoors about 8-10 weeks before you expect the last frost in your area.  They can be planted in egg cartons, Styrofoam cups and other types of containers.  Some people use fluorescent lighting on them but most keep them in a sunny window where they will have the most sunlight.  The vegetable packets will give you dates for starting them inside and when to plant them outside. 

The first thing to do is to determine how much room you have to plant.  Keep in mind that gardens needs lots of sunshine.  You can plant directly into the ground or I know of some people who are doing raised gardening in built up planters.  If you have any trouble bending or reaching long distances, the built up planters can be a good choice.

Once you know how much room you have to plant, then you can decide what you want to plant.  There are so many varieties of items.  If this is your first time, you'll want to choose things that are pretty easy to grow and of course something you like a lot.  Lettuce is a good item for your garden as well as tomatoes, beans, carrots and there are so many varieties and choices for each especially when shopping on the internet.

You will need to determine how much room each of these plants will need and that will be on the seed packets as well.  Once you have that all figured out then you can pick your seeds and start them inside or wait until you can plant outside. 

You may want to put some type of border fence around the garden to keep out the bunnies and other animals that just love new plants.  There are several types to choose from and you can find them online at most garden stores, big department stores and hardware stores to make shopping even easier.

There will be watering and weeding required to grow strong, healthy, great tasting plants.  It's worth the work and the savings to grow your own not to mention the health benefits from the exercise you'll be getting!  Enjoy!