Identify the angles. The origin of the polar plot represents the position of the luminaire. Usually, the origin is not centered on the plot, but offset to show the light distribution for one half of space.
Find the radial scale. The distance from the origin will be illustrated with a series of concentric arcs about the origin. Each arc will be labelled with a value, almost always representing lumens, a measure of light brightness.
Investigate the shape of the curve, finding the radial distance for a given angle. For example, at 0 degrees, straight down from the source at the center, the output curve will be a certain distance from the origin. That represents the brightness of the source when viewed from straight underneath.
Follow the path of the curve, noting the value at each angle. The value of the curve --- the radial value at each angle --- represents the brightness of the source when viewed from that angle. An incandescent bulb, for example, would be almost a circle, meaning it's just about as bright when viewed from every angle. A spotlight's curve will be shaped somewhat like a daisy petal, with a high value at 0 degrees, maybe half that value at 15 degrees, then going to zero by 20 degrees or so.
Note the presence of any additional curves and look at the legend to interpret the distribution. If there is only one curve, it means that the light distribution would stay the same as the luminaire was rotated. If there's another curve, say one labelled "90 degrees," that represents how the light would appear if the source was rotated by 90 degrees.