You can use discarded materials to make a low-cost raised garden bed. Choose a site for the bed that's level and free of debris; then use a tiller to turn and loosen the soil. Even though you're building a raised bed, the roots of any larger plants will go down into the soil below. Raised beds are beneficial because the deep, loose soil helps roots develop more quickly. Strong roots means healthier leaves and fruit as well as fewer disease and pest problems.
There are just a few things that you need for a raised bed: something to hold in the soil and the soil itself. Salvaged pieces of concrete can be salvaged to use as a border. Scrap concrete is heavy enough to keep a garden bed in place for a long time, and best of all, it's free: the only cost is some time and effort to move them into place. Once the raised bed border is in place, you'll need to find some soil to fill the new vegetable bed.
Vegetables need soil that's roughly half dirt and half compost. The county dump is a great source of materials that a lot of people don't know about. They often have piles of compost that's free if you pick it up. Mix equal parts of dirt and compost to make the garden soil. If you have clay soil, you may need more compost than dirt to make it lighter and more aerated; if, on the other hand, you have sandy ground, you may need to add more soil to keep water from draining too quickly through the bed.