NAVIGATIONAL TOOLS USED BY COLUMBUS
The most important tool used by Columbus in his celestial attempts was the quadrant. This was a metal plate in the shape of a quarter-circle. From the center of the circle hung a weight on a string, that crossed the opposite edge of the circle (see figure 1). The navigator would sight the North Star along one edge, and the point that the string crossed the edge would show the star's altitude, or angle above the horizon. (In the case of the North Star, this is always pretty close to your latitude). Many examples of quadrants survive in maritime museums, and often have several scales along the edge. For example, in addition to the angle, you might also read the tangent of the angle from the quadrant. The tangent scale is useful if the quadrant is to be used for architectural purposes.
Columbus also carried an astrolabe on the first voyage, which is somewhat similar to the quadrant. The astrolabe was a complete circle of metal, and had a moving arm (or alidade) that the navigator would sight along to find the star's altitude. Columbus tried to use the astrolabe once, but was stymied by bad weather, and he never used it again. Both the quadrant and astrolabe are dependent upon gravity to work, so they can measure only vertical angles. The quadrant was accurate to about a degree or so, and the astrolabe was a little less accurate.
Time aboard ship was measured by a sandglass (or in Spanish, ampoletta). It was the responsibility of the ship's boy to turn the glass every half-hour in order to measure the time until the watch changed. Since the sandglass was always running a little slow or fast, it was checked daily against the times of sunrise, sunset, or midnight. Midnight could be determined by using a nocturnal, a nifty little tool which tells the time of the night by the rotation of stars around the celestial pole.