Four steps are required to check brickwork as it is being built:
These checks should be carried out as each course is laid and in this order to ensure that the previous checks are not 'disturbed'.
When building any wall, it's necessary to keep the courses at the corners at the same height. A gauge board is used to to this.
Mark out a piece of timber with marks corresponding to spacing of one brick height plus the thickness of the bed joint (normally a total of 75cm).
Use the rod at the corner when each course is begun and check that it is at the correct height, On uneven ground, start by putting a datum peg next to the wall so that the gauge rod can be easily positioned.
Use a spirit level to keep the courses level. Remember that the corner bricks have been set to the correct height, so any adjustment should be by bedding down the bricks in from the corner. Bricks are not made to very tight tolerances, so don't waste your time trying to get each brick exactly level, the point is to get the parts of the bricks which touch the underside of the spirit level, level.
Don't worry about trying to get the bricks level widthways.
Check that the wall face is vertical by using a spirit level, tap the brick across the wall as necessary to adjust the brick as necessary. Do not try to do this to both sides of the wall, choose one side as 'the face' and just plumb that side.
Do it along the wall, spacing the points approximately just under the length of the spirit level.
Check both sides of corners.
Straighten the course by using a straight edge between the points previous plumbed. Tap the bricks as necessary.
Like plumbing the wall, only check the face of the wall, don't try to straighten both sides.
Again the problem of the shape of the bricks come into play. It's unlikely that the straight edge will touch each brick across its whole face, try to get the centre of each brick to touch the straight edge and the two ends of the brick roughly equally spaced from it.