You probably have the usual half-circle protractor:
http://images.google.com/images?hl=en&q=protractorThese usually have a circle-center point, like a hole or crosshairs, where the center of the circle or the angle should go. Put this center point over the vertex of the angle that you want to measure.
Rotate the protractor, as needed, to put one of the zero lines on the line for one side of the angle. (You might have to take your ruler and draw the angle's sides a bit longer, so the sides go far enough to reach the tickmarks on the protractor.) Once you've got "zero degrees" on the one side of the angle, read off the angle number where the other side of the angle passes under the protractor. Some protractors have numbers going in both directions; make sure you're counting from the zero where the angle started.
Here is a video lesson that might help:
http://www.mathsisfun.com/geometry/prot ... using.html