The USDA determines hardiness zones every year and lists them on their website; it also lets you zoom in on your state. Your local garden center will be able to help you choose the right plants for you, and the information's often on the back of seed packets.
In general, you probably want to test before you plant in the spring, and after you finish harvesting in the fall. But if you've never tested before, there's no time like the present! You can also send your soil to a lab for more thorough results, but unless you try this first and still have trouble, or are an experienced gardener who's obsessive about your soil, you probably don't need to go that far.
Those are things you'll probably want to ask around for at your local garden store at first; but eventually you might want to set up your own compost tumbler.
It's very straightforward, where you grow in several square-foot-divided areas, instead of in traditional rows.
For example, corn makes good climbing material for peas and beans, while the wide leaves of squash hide all of the roots from getting too much sun.
The trowel will be your main workhorse, but the transplanter (the one with the measuring marks on it) will make all the difference when you need to measure the right size holes for different plants, and the cultivator will loosen soils that end up packed over time. And gloves, of course, keep your hands clean and protect them from spiky thorns. (These are just starters of course; if you're looking at a big project, you'll definitely need more/different tools!)
Always snip them between two sets of leaves, as close as possible to the bottom set. Make sure to leave at least two or three layers of leaves on your plant, though! This encourages your plant to send out more leaves.
This goes especially for basil and mint! If they put their plant energy into flowers and seeds, they'll have less of it to make leaves.
In your dream garden, you'd get almost two inches of rain in weekly afternoon showers, but we know that never happens. Read more on Gardening Know How, because it's a little more complicated than that; containers may even need daily waterings, depending on where you live.
Weeding's annoying, but if you devote a few minutes a day to it, or try to do it at least once a week, you can catch the weeds when they're young, and it'll be easier to pull them up.