Protractors are typically used either to measure existing angles or to draw new angles. Most protractors are shaped like semi-circles, with a straight side and a rounded side. They are usually made from transparent plastic, with black markings on the surface to indicate various measurements. There are, of course, exceptions. Some protractors are made from metal or other materials while some are shaped like a full circle rather than just half of a circle. For the purposes of this explanation, however, we will stick with the half-circle type.
How To Draw An Angle With A Protractor
1. Draw a horizontal line on the paper. Place the hole in the center of the straight side of the protractor directly over the end point of this line on the side where you want your angle to be.
2. On the upper edge of the rounded side of the protractor, you will see that there are two sets of numbers, each counting upward from 0 to 180 from opposite sides. The set of numbers that you use for your angle is determined by the type of angle that you are drawing. There are three basic types of angles:
- Right angles, which measure 90 degrees,
- Acute angles, which measure less than 90 degrees
- Obtuse angles, which measure greater than 90 degrees.
That means that if you are drawing an acute angle, you will use the numbers that are under 90, whereas if you are drawing an obtuse angle, you will use the numbers that are over 90.  Make a mark on the paper next to the correct number.
4. Remove the protractor and draw a line between the mark that you just made and the end point of the line where the protractor was placed. This will give you your finished angle.
How To Measure An Angle With A Protractor
1. Place the hole in the center of the straight side of the protractor over the center point or vertex of the angle that you want to measure. Make sure the horizontal line at the base of the angle is perfectly lined up with the zero line of the protractor. 
2. Look at the other leg of the angle to see where it intersects the rounded side of the protractor. If it is not long enough, extend it out with a pencil or lay a piece of paper along the line to make it long enough to measure. Write down the number that appears at the point where the line crosses the edge of the protractor. If it is an acute angle, use the numbers that are under 90 degrees. If it is obtuse, use the numbers that are over 90 degrees. This will give you the final measurement of your angle.
This concept is far easier to understand if you can see it in action. Here is a great video that demonstrates step-by-step how to use a protractor: