1. Start small. It's better to grow a few veggies well than try to grow a bunch, do it badly, and get no harvest at all.
Containers are easy and great, and you can grow almost anything in a container that you can grow in the ground. See this post on a lady who grew a great crop of butternut squashes in containers.
Besides, as the old adage goes, it's not how big your garden is; it's what you do with it that matters.
2. Start a compost pile. It's easier than you think. You do not need to buy one of those expensive but nifty fermenter boxes.
To make my compost pile last year, I took the box that our TV came in last year, made it round instead of a rectangle, and surrounded it with stakes and nylon chicken wire that we already had in the garage. (The chicken wire and stakes had been used as a temporary dog run while my parents and their pooch visited.)
Then, I dumped lawn clippings, leaves, shreds from the paper shredder, and kitchen waste in there. You should aim for a mix of about half "brown waste" (dry waste: paper shreds, shredded leaves, etc.,) to half "green waste" (lawn clippings, manure, kitchen waste. Do not try to compost banana peels. They don't ever degrade. Do toss in coffee grounds.)
Good composting article at HGTV.com here.
3. Mulch. I saved last year's leaves in big, black bags to use as mulch this year. You can use just about anything as mulch: shredded bark and wood that you buy in a home store, pine needles if you have a pine tree that sheds needles, or hay or straw from a feed store (very inexpensive, a bale is cheap, cheap, cheap.) Good article on mulch here.
4. Water if necessary. Water deeply and in the morning. If it's rained and the soil is nicely damp, skip watering.
5. Start with easy plants. Really, just about anybody can grow a bumper crop of zucchini, carrots, radishes, or butternut squash. Personally, I'm not ready to grow tomatoes. I respect gardeners who do, but I know my skills and time aren't up to it.
6. Tend often. Tending ten minutes a day, say right when you get home from work, is much better than two hours on the weekend. Stop by your plots, gather a few weeds, scoop some soil up higher on the squash hills, dump some water on anybody who looks dry, and go in the house.