Bricks are often set end-first and tapped to "bed in" before continuing. When laying a brick next to an existing one, apply some mortar on both ends of the brick you're about to lay. If mortar squeezes out from under or between the bricks, use the trowel to remove it.
Place the first brick at the far end and tap it gently to "bed it in." Abut the next brick to the first by filling the gap between them with mortar and then "buttering up" the joint. Iterate with the help of the string line. Put a brick with its side against the wall where you want the pillars to begin.
Four bricks are stacked in a block, then the block is turned by 90 degrees, and the process is repeated. Two-brick stack bond is another option; in this configuration, the next two layers are offset by half a brick. The term "double stretcher bond" can be used to describe this.