The vernier scale consists of two scales.  A stationary scale and a sliding scale.  The two scales are what allow the user to measure with an accuracy of .01 mm.  The stationary scale that consists of the body of the caliper looks like a normal ruler with each line marking one millimeter.  The sliding scale measures to the tenth or hundredth of a millimeter.  To find out the value of the sliding scale you look for the line that lines up with a line on the fixed scale.

In the example above, the 0 line on the sliding scale is between the 11th and 12th millimeter line so you know the measurement is at least 11 millimeters.  Then looking at the sliding scale, only the 4th line lines up with a line on the fixed scale so the value is .4 mm.  The two values combined give you the measurement 11.4mm.  The sliding scale will tell you how accurate it is.  In the example it shows on the sliding scale it is accurate to 0.1mm.  A sliding scale with double the lines would be accurate to .05mm.

Varients of the vernier caliper are the digital caliper and the dial caliper.  The digital caliper makes reading measurements quick and easy as a digital LCD shows the measurements.  In addition, the measurements can easily be converted from inches to millimeters.