Instructions
Steady your quadrant in a stable position, so that your plumb-bomb hangs straight down. While at sea, early mariners used to do this by hanging the quadrant in the rigging of the ship.
Sight along the quadrant's straight edge with the curved edge facing down, such that you are looking directly at either the noontime sun during the day, or Polaris the North Star at night. Both require clear conditions, and staring at the sun obviously entails risk of personal injury.
Mark the angle where the plumb-bob string rests. This angle will correspond to your latitude - if the North Star is 48° above the Northern horizon, than you yourself are at 48° North.
Adjust your navigation accordingly. When sailing through vast bodies of open water, early mariners used to practice "latitude sailing", by which they'd simply maintain the same latitude the whole way across the ocean.