Small yards lend themselves well to growing many plants vertically. With a small investment in privacy lattice panels or wooden stakes, you can train your cucumbers, perhaps a grape vine, a blooming clematis, wisteria or thunbergia to grow vertically instead of sprawling on the ground and taking up unnecessary space. You can save even more money if you plant vining plants against an existing fence or unattractive building such as a garden shed. Plant your vine 6 inches to 8 inches from the structure and then drive nails into the wood every 12 inches, tie string to them and use the string to secure your plants.
You needn't be nervous about starting your small-space garden from seeds. You'll find far more variety when you browse through seed catalogs than when you shop for plants at your nursery, and seeds cost a fraction of what plants cost. If you own a few old flowerpots, whether they're plastic or terracotta, you can use them to start your seeds. Purchase a good quality potting soil---you won't need much---and fill your pots with it. Plant seeds according to packet instructions and then keep your pots in a sunny area where they will be protected from frost. Keep the potting soil moist and then transplant your young plants to the garden when they are about 4-inches to 6-inches tall, depending on the type of plant.
You can easily make your own nutritious compost by creating a pile using lawn trimmings, chopped-up plant parts, kitchen waste and other organic materials. If you start your pile in fall, by spring you will have a good amount of free fertilizer that you can mix into your soil before you plant your garden. If you choose not to make your own compost, you can purchase a large bag of this organic soil amendment at a garden-supply shop for very little money. Only one bag of compost will cover a planting area about 3 feet by 6 feet in size: after you mix it in, you'll have a garden bed that will support almost any plant you choose to grow.
When you choose plants that are drought-tolerant, as are many native varieties, your water bill will remain in check, even during the hottest summer weather. Many drought-resistant plants have pale gray-green foliage and some have attractive flowers. Consider penstemons, clarkias, California poppies (wherever you live) and perhaps one or two flowering shrubs, such as a native lilac. Instead of wasting water by spraying it all over your yard, purchase an inexpensive soaker hose and run it like a snake through your planted area. The water will seep slowly from its pores and water just the area where it lies without watering your driveway, pathways or unplanted areas where weeds will grow if they receive water.