I've seen many kinds of gardens--from tiny window box and container gardens that grow a few tomato plants and green onions to acres and acres of every kind of produce known to man. For newbies who may be intimidated by all of the stuff a garden store presents or for those who are broke, an alternate way to begin your garden might be growing produce scraps.
Most kids have done the "grow an avocado tree from an avocado seed" thing. And for people who have bought potatoes from a seed catalog only to see that they were, well, potatoes that were cut up, it's good to know that many garden items--from onions and garlic to potatoes and ginger--can be bought at your local produce market/grocery store, tossed into a pile of dirt in the backyard, and harvested a couple months later.
Check out these resources for growing a garden from produce scraps that you would otherwise throw away here, here, here, and here.