Build a solid foundation for any brick wall. Dig a trench with a shovel twice as wide as the wall and as deep as at least one-third of the finished wall height. Compact gravel in the bottom of the trench and fill it with concrete. Level the concrete with a mason's trowel.
Start reinforcing in the foundation for some wall types, built with two courses of bricks separated by a space, usually about the width of a brick, to be filled with grout. Set steel reinforcing bars in the concrete vertically in the center of the two brick sides. Space them about every third brick horizontally or every 4 feet, depending on the height of the wall. Fill the gap between bricks around the rebar with concrete grout once the bricks are laid.
Reinforce shorter walls of two courses of brick laid side by side with bars laid in mortar joints. Use 3/8-inch rebar, which is the width of a normal mortar joint. Lay rebar lengthwise, along the long dimensions of the brick for lateral or end-to-end bracing. Set short sections of rebar across two bricks. Cut rebar with a metal chop saw to about 6 inches, which will fit inside the mortar joints.
Use Z-type reinforcing ties for support both across and along a double brick wall. Cut rebar into about 10-inch lengths. Bend each end at 90 degrees, but in opposing directions so the rebar resembles a Z. Bend rebar by putting the end into a vise or other solid holder and pushing it down; rebar bends easily. Lay this rebar across the two brick courses with one end pointing in each direction.