Cleaning dried cement off brick can be a chore. If you drop wet cement onto brick while working, stop whatever you are doing and wipe off the cement while it is still wet if at all possible. Once cement has dried onto the brick, it will be substantially more difficult to remove. It's not impossible, though. There are several steps that you can take to remove dried cement from brick.
Knock off the cement with another brick. If the brick hasn't yet been used in a construction, knocking another brick against the cement may be enough to dislodge it from the surface.
Brush the area with a wire brush. For small amounts of cement, a wire brush may take the cement off the surface of the brick. Move the brush firmly over the cement. It will take quite a bit of pressure. Avoid getting the brush directly on the surface of the brick as much as possible to avoid damage to the brick.
Chisel it off. If the cement won't come off with a wire brush, it may take a bigger tool. Place the tip of the chisel blade against the edge of the cement. Tap the bottom of the chisel with a hammer to knock the cement away. It may come off in one big chunk but will more than likely come off in little pieces. Chisel away from you and watch for flying bits.
Use a commercial cleaner, like Sure Kleen. Before using cleaner on brick, saturate it with water. This will keep the cleaner from absorbing into the brick. Wear heavy-duty gloves and soak a mason's sponge in the cleaner. Hold the sponge against the cement for about 5 minutes. This will soften the cement. Once softened, use the chisel to remove large pieces and the wire brush to remove the leftover bits.
Burn it off with hydrochloric acid. Hydrochloric acid is both more harmful to the brick and more dangerous to use than other cleaners, so it should be used as a last resort. Dilute the acid with about 10 parts water to 1 part acid, and soak with a mason's sponge. Chisel and wire-brush the brick to remove pieces. When using acid, use heavy-duty gloves and goggles, cover every part of your body and be very careful to avoid spills. The acid will damage most surfaces and kill plants.
Rinse the brick thoroughly. If you are using a commercial cleaner or hydrochloric acid, have rinse water on hand. As soon as the cement is removed, rinse the brick completely. Leftover acid will damage the brick. Even if you have removed the concrete through a wire brush and chisel alone, rinsing the brick will remove any leftover dust and debris.
Both commercial cleaners and hydrochloric acid release dangerous fumes. Wearing a protective face mask will prevent inhalation. Be careful disposing of hydrochloric acid and commercial cleaners. They are hazardous waste. Contact a hazardous waste disposal site in your area to find out how to safely dispose of the substances.