Construct a mobile trellis for use on the brick wall; some plants and vines can't "grab" the brick on their own, and need something like a trellis to climb. Make use of a trellis over the lower portion of the brick wall to give you more control over the direction and look of the growth of climbing plants that easily attach themselves to brick. Set decorative 5-gallon pots or containers at the corners of your brick wall to act as supports for this trellis.
Mix quick set concrete in a bucket to the side, per the directions on the package. Put a 4-to-6-foot stake in the first decorative pot and pour concrete in around it. Hold the stake straight while the concrete hardens. Repeat this process with the second stake and decorative pot. Allow the concrete to cure for 12 to 24 hours.
Cut a length of trellis netting to stretch between the two stakes. Use twine to tie the netting securely to both stakes every 3 to 4 inches from top to bottom.
Thread a piece of wire through the loops along the top of the netting to support the trellis. Tie the wire to the stakes at the end and secure it. Repeat this process at the bottom of the netting as well.
Plant vines in front of the trellis. Choose sun-loving flowering vines like bougainvillea, trumpet vine, clematis or passiflora for sunny areas. Choose shade-loving plants like ivy cultivars for shady areas.
Prepare the soil in each planting spot to loosen it and add nutrition. Mix 6 to 7 inches of organic compost into the top 10 to 12 inches of soil, then plant the vines in the amended soil. Plant each vine with its crown just at soil level. Ideal planting times are early and mid-spring, after the last frost but before the heat of summer.
Tie the vines of your plants loosely to the trellis in upward and outward formations for an eventual full coverage of your trellis and the brick wall. Use soft twine for the ties and tie only on the woody or main vine sections. Keep your ties loose to avoid cutting into the plant matter.
Test the soil for moisture every week. If the top 2 inches of soil are dry, water the vines with 2 inches of water to moisten the topsoil. Lay mulch over the soil around the vines, but leave 2 inches of space between the vines' bases and the mulch for fresh air.