Add hot water to a bucket. If the bricks are exceptionally dirty, add one small squirt of plain, undyed dish-washing soap to the water.
Dip the brass brush into the hot water. Start at the top corner of the wall and begin scrubbing. This is a hard brush, but it should not damage the surface of the brick. If the wall is very dirty, you may need to apply a lot of elbow grease. Work one brick at a time and move to the next when the previous one is completely clean. Frequently change out the water so it is always hot.
Scrub the grout lines. Use a softer bottle brush to clean between the bricks on the grout line. If the grout is very old, it may not come completely clean. If this happens, add a new, thin covering of grout between the bricks to make it look better.
Repeat the cleaning if necessary. Depending on the age and condition of the bricks, you may need to repeat the scrubbing process to completely remove old dirt and grease.
Apply a brick sealant over the bricks once they have completely dried. You can use a regular paintbrush. Start at the top corner and work throughout the wall.