Learning to navigate with a Compass is easy, but first you need to understand that having JUST A COMPASS will not do you any good without knowing which way you want to go.
What you need to navigate with a compass: 1) Compass (the one shown is good enough)
2) Road Map of the area you are
Why the road map?
Let me explain.
A compass can tell you which direction is North, South, East & West, but it doesn't tell you where the roads are. A road map does.
If you have a road map of the area you are in, then you can figure out about where you went into the woods and then you can see where the roads are. If you don't know, then ask BEFORE YOU GO INTO THE WOODS. Roads mean vehicles and help when you are lost - AND - they are a MUCH easier way to walk to get to a bigger road for help.
So your directional goal should be to head for the easiest road you can find. What you are looking for are good North/South or East/West roads that run the entire one side boundary of the area you are in. Then use your compass to situate yourself in that direction and go!
The accuracy of a cheap compass be enough to get you in the general (maybe not exact) direction.Even if your compass is off a few degrees - you'll still hit your boundary (road). Then your road map will tell you which way to go on the road.
Small roads are the same principle - if you have no idea what road you are on, pick one that runs into the general direction of a main road. Once you hit a crossroads, there should be some type of sign to help you out. So it's not the compass that tells you the direction to go, but it's having a compass and map that will tell you where you need to go.
MAP QUEST! Map quest makes it easy to get a up to date map of the local area. You can pin point where you are going very well and give yourself some great info if you need it. Then print out a couple pages and stuff them in your pocket.
Remember: The top of the map is NORTH.
EXAMPLE ONE: Here's an example using Map Quest.
If you get lost and are at "
X1", then you want to go west to hit Hwy 1054. This is easier than going north as you have a definite north/south boundary.
If you are at "
X2", then you want to go south to hit Hwy 1054. You don't want west to Hwy 1054 by itself because if you are farther north than you realize, you could miss it.
Same goes for going to the east as Broad Ford Pike may turn and you would miss it.
The other thing here is if you go south and hit "a road", if the train track is close, you know you're on Hwy 1054, then you pick north or south.
If not, you're on Broad Ford Pike and want to turn west down the road to hit the "bigger" Hwy 1054 road. But walking down Broad Ford Pike will be easier and walking in the woods.
GO FOR DEFINITE BOUNDARIES THAT YOU CANNOT MISS ! 
Map 2 is a closer in view of the same area.
Hwy 1054 runs north to the town of Morgan. So when you get to Hwy 1054, you're going to go north towards town.
TOTALLY LOST! - EXAMPLE TWO: Let's say you have no idea where you are!
Looking at the 2nd map, you want to go.....west!
Why?
Because the train track runs the full length of the area going north and south. I'll either hit the track or Hwy 1054. If I hit just the track, I turn south to Morgan. If I hit 1054, I go north into Morgan.
IF I'm totally turned around and I happened to already be west of the tracks and Hwy 1054, I still have a good chance of hitting Hwy 330 as an alternative boundary. Even if I hit a smaller road (like the south end of Hwy 330), I still head north on it till I hit 330.
IF I do hit 330, I'm going to have to wait till I see a sign for 330 (south of Morgan)or for 330/1054 (north of Morgan)to know where I am. This time I may have to back track to get to town, but at least I'm no longer lost!
So to recap, the compass tells you the direction you are going, but you need a map to tell you which direction you WANT to go. Group Tactics If you are a group leader, take a moment and have a short orientation meeting with your group at the beginning of any outdoor trip. Since everyone will not have a map or compass, go ahead and show everyone the general area where they are.
Setup a plan if they get lost like "go west till you get to Hwy 1054, then go north to Morgan".
Not only will this give everyone the same goal, but it will also help in rescuing someone that is lost by giving YOU a place to find them - i.e. on Hwy 1054.
Now if everyone is carrying their cheap little 4-1 tools or their compass, they'll know the direction and which way to safety : )

Ironhand