Where?
For some reason many people seem to find the sight of their vegetables to be less than aesthetically pleasing. We have been conditioned to believe ideal beauty is a “clean” lawn surrounded by geometric beds of perfect flowers, no matter how unproductive and ultimately pointless it is. Too often vegetable beds are stuck up at the end of the yard, away from the house and the water supply. These gardens are usually ignored, infested with weeds, and full of slugs, spiders, and snails.
To make the most out of your garden you need to position it with three things in mind: sun, water, and access.
Plants need at least six hours of sun per day; many types will need more than that. Watch your garden and work out which areas get the most sun. Many houses are built to take advantage of the sun so that the best place for your garden may well be right next to the house. This is ideal as you will then have a close supply of water for your plants. You'll find weeding is much easier. Just stop and remove a couple of weeds each time you pass by and you won't even notice the aches and pains. And come harvest time, you will spot the ripe fruits before the birds do.
What?
I grew zucchini in my first year of gardening. I realised about halfway through the summer as the first fruits were coming ripe that no-one else in the family would eat them. The compost pile did very well that year. A little planning would have saved me the wasted effort. Have a look at what vegetables and fruit your family eats regularly. In terms of saving money, it may well be that your favourites will be cheapest in the shops at the same time as you harvest at home. Never mind. Home grown will always taste better.
If you are a complete beginner, start with the easier plants. Carrots, radishes, tomatoes and potatoes do well for many beginners. Of course, it will depend on your climate. If there is a little bit of shade, lettuces and salad greens will probably be good for you. You have to realise, though, that for most of us gardening is not an exact science. You will go through a bit of trial and error before you get things right for your patch. It is probably best to concentrate on doing a few things well at first rather than spreading yourself too thin and growing lots of things poorly. Build your skill set one step at a time.