Acquire small cuttings of succulent plants you like by either purchasing them from a garden center or cutting them yourself off established plants. All of the cuttings should be about the same size.
Find a container suitable for your wall garden: a shallow wooden crate or an assembled wooden frame. Build a frame yourself, or buy one from a nursery dedicated to succulents.
Staple a piece of chicken wire or wire mesh over the frame.
Fill the frame with potting soil by pouring it through the wire.
Place your cuttings into the holes in the mesh. Place them close to each other so they will grow together and hold in place over time. Create patterns out of different succulent types, or place them randomly. Fill in the spaces between the succulents with moss to hide the soil.
Allow the succulents to grow in the frames on a flat surface for at least six weeks so the roots will take hold and keep the plants in place once you hang the frame or box.
Mount your vertical garden on a wall either using the hardware from a frame kit, or L-shaped brackets appropriate to the weight of your finished piece.