Decide on a color, style, size and pattern. Bricks come in various colors from white to deep red, with smooth faces or with textured sides, usually 2 by 4 by 8 inches -- and can be laid in many patterns, although an overlapping or running bond is most common. Measure the wall with a tape measure and order enough bricks; you need five standard bricks per square foot. Get extra to allow for cutting and mistakes.
Ensure there's a brick ledge at the bottom of the wall, a 6-inch wide strip of concrete, usually poured as part of a foundation. Dig a 6-by-4-inch trench the length of the wall with a spade if there is no ledge, fill it with concrete, level the surface with a trowel and level and let the concrete cure for a week.
Cover a wood-sheathed wall with a moisture membrane, fastened with a construction stapler. Install metal flashing over the ledge at the bottom of the wall and around any doors, windows or other openings. Mix mortar according to directions on the package; it should be firm enough to stand alone, but thin enough to spread easily. Lay 1 inch of mortar on the ledge and press the flashing down into it, with one side up against the wall. Nail door and window flashing to the sheathing with roofing nails and a hammer.
Start laying bricks at the bottom of one end of the wall, usually the right side if you are right-handed. Use a chalk line and line level to snap a level line about 4 inches up the wall as a guide for the first layer or course of bricks. Spread mortar on the bottom, back and one end of the first brick and set it in place. Ensure it's level and firmly in place; leave a slight gap between the brick and the wall sheathing.
Add bricks, putting mortar on the bottom, back and ends of each brick, 3/8 to 1/2 inch thick. Put short sections of rubber tubing in the vertical joints of the first layer about every 24 inches or three bricks, to form weep holes to drain away any water that gets behind the brick façade. Remove the tubes when the wall is done. Check the brick level every few bricks. Lay one course to the other end of the wall.
Start the second course with a half-brick. Use a masonry saw to cut a brick in half or snap it by scoring it with the point of the trowel around the brick faces and then tapping it with the trowel handle until it breaks. Lay the cut end of this brick to the inside, with the factory edge at the end of the wall. Add bricks in courses along the wall, checking regularly to make sure they are level and straight along the wall. Start every other course with a half-brick.
Install wall ties starting with the sixth course of brick. Nail one end of these corrugated metal straps to the wall and place the other end at a 90-degree angle into a horizontal mortar layer between bricks. Place ties on every stud and every 16 inches vertically to conform to building codes. Keep the mortar joints equal the length and width of the wall.
Put steel lintel bars above door and window openings to support bricks above. Extend lintels at least 4 inches or half a brick into the mortar joint on each side of the opening. Pause a few courses below the top of the wall and measure the gap. Adjust the mortar joints slightly to finish the wall with full bricks, to avoid having to make any lengthwise cuts.
Shape mortar joints every course or two, depending on wall length, with a steel finishing tool. Work before mortar sets up. Press the convex end of the tool into the mortar to force the joint into a concave, which will drain water away from it. Dampen the end of the tool if necessary to make shaping easier. Shape both horizontal and vertical joints and wipe off any excess mortar with the tool and a damp sponge.