This is the art of not being lost. Ok a little humor here but it is a serious subject. It is important to maintain correct orientation at all times for several reasons, and you need to know where north is at all times.
Knowing this information permits you to know the other cardinal points which in turn makes it possible to navigate more accurately than to haphazardly go along hoping to make it to your destination.
A map and compass if you have them will help you enormously. It can happen through no fault of your own if you do not have these important items because it depends on the emergency and the circumstances. Prepare whenever possible, but things happen at times that will demand more of your talents and so forth.
Therefore prepare yourself to have a backup to enable you to navigate without a compass, and learn to map the region that you are in if out in the woods. If you are on a trip and something happened, having a good pre-trip plan where you would know the region very well before heading out will be extremely beneficial to you.
If you have a GPS it can be good but know its limitations. Conserve battery power as much as possible and use it in combination with a map for position fixing. It also requires you to know BEFORE going out on a trip how to correctly use your GPS receiver. Every company and model have their own features and particularities, so even if you had a GPS and knew how to use it, if you bought another model get acquainted with how it works. It isn't time to fiddle around learning how to use it when you are in an emergency and you need to conserve precious battery power.
If you are lost and do not know your present point of location or only know your approximate location, stay right where you are for starters. If you were involved in an accident of some kind such as a plane crash or other, follow the order of priorities and make the judgment call of if and when to leave when the time is right.
No matter what, avoid making a decision to move or relocate if you weren't cool, calm and collected at the time of making that decision. Doing otherwise would be unwise and could lead to far greater problems ahead. It may cost you your life and that of anyone else in your group if they went along with the decision. Have a look at Static Survival and Roaming Survival on this page for more information.
In determining where north is without a compass there are several methods, the most accurate being the sun. Plants, trees, animals and insects can be used as well though not very accurately, and it requires the knowledge of how plants and trees grow as well the behavior of animals and insects.
You will hear at times that you can tell where north is by the moss growing on a tree. The problem is that moss sometimes grows all the way around. No help there. I have seen it and know that it happens. However, one time I have used moss as a clue when it wasn't growing all the way around the tree as well as other clues in the forest and was able to find north. A few times when I have tried it I was able to find north just by looking at my surroundings but also failed at other times.
Use several methods to gather as many clues that you can to have the best chance at getting it right.
However, it isn't easy because things change or are different in the forest. It is as though the rules aren't respected.
An example is that in the northern hemisphere we are taught that trees and plants tend to grow more abundantly toward the south or direction of the sun.
However due to disease, storm damage and prevailing winds trees often have less branches and leaves towards the south, or prevailing winds blow the trees in in another direction and can throw you off as you try to estimate where north is. Another indicator and example is bark fiber on a tree which tends to be finer on the north side of the tree, but not always.
As mentioned above the sun is the best way without a compass to find north, which will then help you to find other cardinal points for navigation. It can yield a fairly accurate estimate of where north is, and there are many different methods that exist to to use the sun for direction finding. Some are simple and others a little more complicated. I will not get into the details here, but I will give you links to be able to study on the subject.
Here are some of the methods. See the links below.
1. Shadow Tip Method.
2. Shadow Stick Method.
3. Analog Watch Method.
Here are some links to help you learn more about location and navigation.
4. Survival Topics - Stars
Have a look at the Videos page as well for more information on the subject.