Using a watch as a compass
To use your watch as an approximate compass outside of the
tropics in the northern hemisphere, hold the watch horizontal and point the hour
hand at the sun.
Half way between that point and the twelve o'clock mark on your watch points to the south. For example, if it is eight o'clock, point the 8 on the watch face at the sun and south would be at the ten o'clock position. If it is four o'clock, point the 4 on the watch face at the sun and south would be in the two o'clock position. At midday (twelve o'clock), the hour hand itself should point south.
The method of halving the angle between the hour hand and the twelve o'clock watch position is required since the earth rotates once in a day, but the hour hand goes around the clock face twice.
In the southern hemisphere, hold the watch horizontal and point the twelve o'clock mark in the direction of the sun. The north-south line is half way between the hour hand and the twelve o'clock mark.
Using a watch to determine direction within the tropics is more complicated, since there are two solar maxima. The sun may lie to the north or south (or at midday be directly overhead), depending upon the time of the year.
Because time on our planet is divided into 24 broad time zones, the sun is not normally directly south or at its highest point in the sky at exactly midday. The watch-as-compass method is therefore an approximate guide to direction only. The most exact method of finding direction without using a compass is to mark and measure the shadows that occur around midday. The shortest shadow cast by an object always points exactly north.
To find where the sun is on a cloudy day, hold a pencil or stick upright over a light piece of paper or a lighter part of the ground. The stick or pencil will cast some kind of shadow, indicating the position of the sun.