It's All About the Soil
The very best garden investment is a healthy, fertile soil that's the consistency of crumbly chocolate cake. It should be alive with worms, plant-nourishing bacteria, and other tiny microbes that help crops grow. You create soil like that by adding plenty of organic matter; the best and cheapest source is your own compost pile of dried leaves, grass clippings, and vegetable scraps from the kitchen. Letting it all break down into nature's "black gold" takes time, though. To get your garden started, you'll probably need to buy some organic matter to improve fertility.
As soon as the soil is no longer soggy, till under any sod and incorporate a complete organic fertilizer ($5), two 40-pound bags of compost or manure ($15), and, if your soil is acidic, as most tend to be in moist climates, a bit of lime ($3 a bag). Get a simple soil test done through your state's cooperative extension service, or buy one at your garden center. If hand-tilling is too much effort, pay a landscaper a one-time fee to rototill the plot. Keep your beds soft and fluffy by not walking on them. In future years, if you keep the beds weeded, you can fork in compost shallowly and never have to till again.