The compass that you will use has different parts, and each model has a specific way to use it. 

Part 1: Compass Parts.

Military Lensatic Compass.

The military lensatic compass is more complex and more accurate of all the compasses. Its parts are as follows:

Cover and sighting wire: 

Protective cover for the compass dial and wire for sighting on targets for computing azimuths.

Lens and aiming notch:

The lens is used to read the compass dial, and the notch is used in conjunction with the sighting wire.

Bezel ring:

The bezel ring is used for navigating using the center hold method. It has 120 clicks, each of which equals 3 degrees of declination.

Dial:

The compass dial "floats" with the north arrow. To read this dial you determine the angle in degrees under the thin line on the glass covering the dial. On a military compass there are two separate sets of measurements. 

The outer ring (Black) is marked in mils. This is used in computing artillery and direct fire adjustment adjustment. You should not use this in normal land navigation.

The inner ring (Red) is marked in degrees. This is the section you will normally use.

Standard Compass.

The standard compass is less complex and less accurate than the lensatic compasses. Its parts are as follows:

Bezel Ring:

The bezel ring of this type compass also has the degree markings incorporated into it.

North Arrow:

This is the red end of the needle that floats inside the bezel ring.

Button Compass.

The Button compass is the lest complex and lest accurate of all the compasses. Its parts are as follows:

Bezel Ring:

The outer compass ring that shows degrees.

North Arrow:

Red end of the compass needle.

Part 2: Compass hold.

There are two basic methods of compass hold. Compass to cheek which only works with the Lensatic compass, and center hold which works with any compass.

Compass to cheek. Compass to cheek is considered accurate to within 3 degrees.

In the compass to cheek, first form your right (left for lefties) hand into a point.

Slip the bailing wire of the lensatic around your thumb, then curl your index finger around the base of the compass. 

Rest the bottom of the compass on the other curled fingers. Push the lens and the cover together until they rest against each other at the tips.

Put the heel of your thumb against your cheek.

To read the compass to cheek, you match the compass dial in the magnifying lens to the desired azimuth (angle). To determine the angle to a point, you aim the sighting wire on the cover at the target - centering it in the notch on the top of the lens. Then you look down to read the direction (azimuth).

Center Hold . In the center hold method, You hold the compass between waist and chest height. Look down to read the compass dial. Center hold method is considered accurate to within 11 degrees.

To read the compass using center hold method, you turn your body until the compass dial aligns with the desired azimuth (military), or turn the bezel ring on the compass to match the north arrow until your body and the bezel ring align with the desired azimuth (standard). To determine angle to a target, you turn your body to face the target until the compass is lined up with it and read the degree ring (military), or face the target and turn the bezel ring until north on the bezel ring lines up with the north arrow.

Part 3: Accuracy, Why?

The reason the Compass to cheek is most accurate is because you are looking directly at the target sighting it in like a rifle sight, and reading the compass using a magnifying glass to get the most accurate possible reading. This method can only be used with lensatic, and then only if you can get a clear sight to the target. In truly thick vegetation it becomes useless. Center hold is quicker, but less accurate because you are using your best judgment to ensure you are aligned to the compass target and are reading the compass scale using a less accurate method.

What does this difference mean to you. Well we can best describe this using a math. Lets suppose that you are going to walk 1 mile along a specific azimuth. If you walk 3 degrees off, at the end of a mile you will be about 270 feet off your target.

How did I figure that? Well to start with, there are 360 degrees in a circle, we also know that a circles circumference is equal to 2 x radius x 3.14 (Pi). Our circle would have a 1 mile radius, and a 6.28 mile circumference. 

There would be .017 miles in the circumference per degree (6.28 / 360 = .017). So 3 degrees = .051 miles.

1 mile = 5280 feet, so .051 miles = 269.3 feet (5280 x .051 = 269.3).

Now imagine that you are going to use center hold (11 degree accuracy) for 5 miles. You could possibly be up to 4937 feet off target - almost a mile! Accuracy becomes paramount, as well as breaking down your trip into smaller legs to make it more manageable.