Before starting
Remember your directional starting point is always North. On a map, the "North" you're interested in is "True North." On maps that's very easy to find. In the real world, finding True North is pretty difficult so in the field we use "Magnetic North" because the compass needle always points to Magnetic North, and so it's very easy to use in the field.
When working on maps, you'll never need to use the magnetic needle of your compass! So forget the needle and the orienting arrow when working on maps. When working with maps, only use the Orienting Lines and "North" of your compass. On maps, you orient your compass to the map using the Orienting Lines and the North mark of your compass.
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In the field, you will not use the Orienting Lines, but you will use the magnetic needle and it must be centered in the Orienting Arrow by putting "Red in the Shed." Once the magnetic needle is centered in the orienting arrow, your compass is oriented to Magnetic North and the direction you're interested in will be the direction your Direction of Travel arrow points.
Putting it to Use
Let's do an example. In this example, we employ a method referred to as Dead Reckoning (sometimes referred to as ded reckoning for "Deduced" reckoning). That's when you find your desired direction (azimuth) between to points, go to the starting point, find an object in the distance that falls on the desired azimuth, and walk a specific distance using your pace to arrive at your point.
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Determine the Azimuth/Bearing between two points on a map.
We'll use the Ferndale, AR Topographic Map. (60 MB download)
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You want to travel from Lake Nixon to Ferndale crossing. What is the azimuth or direction you must face when walking this?
Carefully and exactly align a ruler on the map between the two points. Hold it steady. Note, if the two points are close enough to each other, you don't need to use a ruler, you can just use the straight-edge side of the compass.
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Place your compass perfect along the ruler so that the Direction of Travel arrow points in the direction you are traveling (from Lake Nixon to Ferndale). Slide compass along ruler until the compass' Orienting Lines are near a grid line. In this discussion, we will assume the Grid North is very close to True North so that using Grid North is a good surrogate for True North. Ideally, we want to use a Line of Longitude for True North. There are only two lines of longitude given to you on all maps; the left and right side. You could draw your own lines of longitude between two identical longitudes from the top and bottom of the map. But in this case, we can use the UTM GRID to indicate True North. Typically, this is acceptable for short distances, but as travel distances increase, any difference between True North and Grid North will result in error. To be safe, always consider the difference between Grid North and True North.
The reason we can use the northerly lines on the grid in this case is because the Declination Diagram shows that GRID NORTH is only 15 minutes away from TRUE NORTH. 15 minutes is only 0.25 degrees: 15' / (60' in one degree) = 0.25 degrees. So the error in using GRID lines for TRUE North is 1/4 of a degree. Most baseplate and mirror compasses aren't even accurate to that level and there could be errors made in drawing your own lines of longitude. So we'll accept this approximation.
On USGS maps, remember the star ★ indicates TRUE NORTH (TN).
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The half arrow ⇀ indicates MAGNETIC NORTH (MN).
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The single line indicates GRID NORTH (GN).
Now, rotate the compass bezel so that the compass Orienting Lines align with the northerly grid lines on the map. Make sure the compass' North is aligned with the map's North.
Read 320° under the index line by the Direction of Travel arrow. That’s the True Heading because it was generated from a map which indicates True North. In the real world, it's not so easy to find True North, but it is easy to find Magnetic North by using the magnetic needle of your compass.
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If your compass doesn't have a declination adjustment you'll need to calculate what magnetic heading to use. Suppose for the sake of argument, the magnetic declination at this location is currently 2° West, the magnetic heading would be 320° + 2° = 322°. You would walk 322° in this case. See the section on Magnetic Declination for details.
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If your compass does have a declination adjustment, make sure it is set to the correct and current declination of the site you're at. If your compass does have a declination adjustment, then you can just keep the True Heading dialed-in and the Orienting Arrow is adjusted to compensate for the magnetic declination. The remaining part of this discussion will assume you have a mirror compass with a declination adjustment properly set for your location.
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Now you go to the starting point you identified on the map. Start on the point as exactly as you can. Use the compass as it was set from your map, with your desired azimuth under the front index line. Holding the compass at eye level and as flat as you can, look just over the top of the compass capsule at the mirror and adjust the mirror angel so you are viewing the compass capsule straight down on its face. Make sure the mirror line bisects the compass needle pivot point. Now, locking in that hand/arm/ body position, rotate your entire body and compass along with it so that you put RED IN THE SHED. This aligns your compass with MAGNETIC NORTH. Your compass' declination adjustment offsets the orienting arrow ("Shed") from the orienting lines (the orienting lines represent TRUE NORTH) by the amount of the declination thus compensating for the offset of True and Magnetic north. With RED IN THE SHED, double-check your alignment and ensure the mirror line is still bisecting the compass pivot point. This is an iterative process, so take your time. With everything aligned and RED IN THE SHED, find an object far in the distance in the sighting notch (at the hole in the bottom of the mirror or the notch at the top of the mirror). Remember that object because you will walk straight towards that object.
Before you start, you may want to turn around and find a tall object behind you so that you can shoot a back-azimuth towards it later to make sure you're on course. If you do that, stay on your starting point and do the exact same thing as before except now you put BLACK IN THE SHED. Remember "Black will take you back." Now that you have found an object on the back-bearing, once you start your journey towards the original object, you can always stop and check that you're on course by checking your back-bearing against that object you just found.
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Find the number of paces you need for the leg and start walking straight towards the object you found in the distance earlier. Ideally, you will find your desired location when you're done with your pace. If not, turn around and look for that back azimuth object you found at the start of the leg by putting BLACK IN THE SHED. If the object is not aligned, make note of where you are and you can move left/right until the object is aligned.
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Practice this often. This helps reduce your error and it will make you more confident in this approach. After some practice, it will make a lot of sense and become second nature.