Adjust the fence on the band saw to make a 1/16-inch side cut. Lock the fence in place.
Place a 2-by-2-by-16-inch scrap board flat on the table of the band saw with one side flush against the fence. Turn the saw on and guide the board through the saw in a steady motion, just fast enough to allow the blade to saw through the wood. Stop the cut after approximately 8 inches.
Place a protractor on the 16-inch edge of the board nearest the cut. Adjust the protractor to the line of the cut. If it is off at all from 90-degrees, the blade has drifted. Adjust the fence to the angle of the drift so that the blade cuts an even 1/16-inch thick slice from the entire board. Place the protractor on top of the fence and adjust it to the angle you measured on the scrap board. Lock it in place.
Lay one 5/4-inch edge of the 5/4-by-8-by-16-inch board flat on the table of the saw. Place one 8-by-16-inch side flat against the fence. Turn the saw on and slowly guide the board through the saw, going just fast enough to allow the blade to cut the wood. As the board nears the midway point in the cut, pick up a push block and position it at the back of the board and guide the end of the board through the saw with the block.
Remove the board and the cut piece of veneer off from the saw. You can cut more sheets of veneer from the board in this manner and turn the saw off when you are done.