Full-scale vertical gardens have a tendency to be expensive, but you can make a patio-sized version for nearly nothing if you use a plain, everyday wood pallet.
Just about any wood pallet will do, if it's in decent enough shape. If you're planning on growing edibles in your garden, you'll want to be sure you find a pallet that's been heat-treated (not chemically sealed), otherwise there's not much else to worry about when choosing one. Along with the pallet and plenty of potting soil, the only other things you'll need before choosing your plants is a small roll of landscape fabric, and a staple gun to apply it to the pallet.
The best part about using pallets is that they're generally free. Grocery stores get rid of them by the dozens, and usually have no problem with giving them to people who ask the management nicely. Just take a truck with you—they're not very kind to the paint on small cars.
While getting the pallet to your house or apartment may be tricky, the whole thing's incredibly simple to put together once you've got your supplies. After sealing off one side of the pallet with the landscape fabric, you fill the inside with soil, and plant your garden. Just place the finished pallet-garden in a spot where it'll get good light, and enjoy some fresh air!
Hit the link below to see more detailed instructions. Photo by Fern Richardson.
How to Turn a Pallet into a Garden | Life on the Balcony via Curbly