Vertical vegetable gardening is the perfect solution for those with limited space. Vegetables can be planted in hanging containers like baskets or upside down tomatoes planters, or in the ground growing up a trellis or wall. And hanging wall garden bags are becoming very popular, too, because they can transform a boring surface into a jungley-looking paradise.
(Not that I would know anything about that, I'm nearing 60 and still wear purple Keen shoes everywhere...)
Vertical vegetable gardening can take many forms, and which you choose will depend on the specifics of your space and the plants you want to grow. A few of the possibilities are:
If you have only a small patio or balcony for vertical vegetable gardening and want to maximize your yield, you can grow vegetables rooted in containers but growing up a trellis or wall. Read the article on container vegetable gardening for general information on pot size, container mixes, etc. Be sure to use a large enough pot - 12-15" diameter minimum.
To trellis a single cucumber or tomato plant in a pot, take three 6-foot-long bamboo stakes (available in packages at Home Depot and other garden centers), and stick them in the pot equidistant around the edge.
Then lash them together at the top with string, wire, or electrical tape, forming a triangular "teepee" frame. As the tomato or cucumber grows up, tie its branches to the trellis with torn strips of old t-shirt or other soft fabric. You can buy Soft Ties at nurseries, but old t-shirt strips work great and are free.
A great trellis for really large pots is a simple cylindrical cage cut from a roll of fencing wire. My favorite for this is 2x4" mesh "sheep fencing". (Though this may be hard to find if you live in the city. I bought a 50 foot roll of it at the feed store, and use it for trellises and leaf bins.) This cage-type trellis works best with fairly vertical-sided pots, like the big black plastic shrub or tree tubs that you can get free from most landscapers or friendly nurseries. For beautiful, rounded glazed-ceramic type pots you're better off with a bamboo-stake type trellis.
To make a single trellis that spans all your pots, you can build two simple A-frames out of 1x2s bolted together at the corners. I've also seen beautiful ones made of branches lashed together. Staple or nail (you know, those little u-shaped staples that you nail in with a hammer) wire fencing (2x4" mesh sheep fencing works great) or sturdy plastic mesh to one or both sides of the frame. This whole tent sits atop your row of pots, and the plants can be tied up as they grow.
If you are on a balcony with another balcony above you, it is simple (but dangerous - have someone hold onto you when you're up on the ladder!) to put screw-eyes into the joists above and hang a pre-made plastic mesh bean trellis down to the pots.
If you want to incorporate vertical vegetable gardening into your regular in-the-ground garden, there are two ways. If you happen to have space at the base of a south-facing wall or wooden fence, an easy way is to buy a 6'x10' sheet of concrete reinforcing wire (Home Depot) and lean it against the wall. You need bolt cutters to cut it, but you can cut it to whatever size you want to fit your space. It is extremely, sturdy, strong, and durable, and I think it actually becomes quite beautiful as it rusts over time. Very "rustic"!
The way I maximize space in my soil garden out back is by making huge, very sturdy cylindrical cages out of this same type of wire. Concrete-reinforcing wire is stiff, 6x6 inch mesh and you can make an endless number of different sized cages out of it.
It works great for growing growing mini-pumpkins, winter squashes, gourds, melons and cucumbers. I bend it into 3 or 4 foot diameter cylinders, cut off the bottom ring of wire so that the verticals can be pushed down into the ground, and then plant my acorn squash in the middle. You have to pay attention and keep training and tying the pumpkin or squash up, because they can grow quite a bit in a day or two! I tie it up to make it grow in a spiral around and around the outside of the cage.
Nurseries and garden centers have recently begun carrying Wall Garden Bags made of heavy nylon with grommets that allow you to hang bags of soil from a wall. They look stunningly beautiful when filled with flowers or sweet potato vine spilling over, transforming boring walls into hanging gardens. I think they are wonderful... although I have yet to see one that was big enough to grow much in the way of vegetables.
They would be appropriate for determinate cherry tomatoes, basil, or other herbs. And never be shy about combining any vegetable crop with flowers, they are so gorgeous together! Try some speckled romaine lettuce alternating with lobelia and trailing petunias.