describing how large an earthquake was
To describe how large an earthquake was, there is always a qualitative observation approach and a quantitative approach. Using the Mercalli Intensity scale is the qualitative observation approach and the Richter Scale and the Moment Magnitude scale are the quantitative approach. The latter two use seismographs to interpret the amount of shaking involved  then computed to describe the amount of shaking.
Remember  the breaking occurs deep underground. This is where the rocks break, shatter, and move as a result of the forces acting on it. This breaking of concrete is a sample model of what it's like going on deep underground.
Going Further: There is a lot more to the mathematics behind faults and the associated stresses. Here is a collegiate level of information concerning the fault stresses. Structural Geology 

The Modified Mercalli Intensity Scale
One way to describe the destruction cause by earthquakes it to use what is called the Modified Mercalli Intensity Scale. This methodology was developed in 1931 by two American Seismologists Harry Wood and Frank Neumann.
Using Roman Numerals, each increase describes the level of damage from the shaking felt. It is not mathematically based, but instead it is based on observational effects & severity.
The lower numbers of the intensity scale generally deal with the manner in which the earthquake is felt by people.
The higher numbers of the scale are based on observed structural damage.
The following is an abbreviated description of the levels of Modified Mercalli intensity.
Using Roman Numerals, each increase describes the level of damage from the shaking felt. It is not mathematically based, but instead it is based on observational effects & severity.
The lower numbers of the intensity scale generally deal with the manner in which the earthquake is felt by people.
The higher numbers of the scale are based on observed structural damage.
The following is an abbreviated description of the levels of Modified Mercalli intensity.
The problem with the Mercalli Intensity Scale (MIS)  is that it is not mathematically descriptive  which means there really is no standard. It's all subject to interpretation. The other problem with the MIS is that it is great for areas of high population  but not for regions with low population.
The Richter & Moment Magnitude approach
Both the Richter scale and the moment magnitude use seismographs in different ways to calculate the amount of shaking involved at the epicenter  or where the shaking originated at the surface. Geologists currently use the moment magnitude calculations over the Richter Scale  but it reflects what Charles Richter started off with.
The Basics of Interpreting a Seismograph
When an earthquake happens, elastic potential energy overcomes the frictional forces and is converted to kinetic energy once the fault breaks and slips. When that happens, large seismic waves are propagated outwards from its source from across the surface and deep underground, and even through the earth. Geologists use a Seismometer to pick up and sense the Seismic waves that are generated as a result. Below are the seismographs and modern seismometers. Modern seismometers are electronic that can then be relayed to computers to keep track of any earthquake activities.
How older seismographs worked was by a mass that stayed put while the rest of the machine moved up and down. The resulting scribble is the wave the traveled through the rocky material the seismometer sat upon.
A seismometer is a device that picks up wave activity from the earth. It's much like a microphone that we put on the ground. A microphone senses waves from sounds generated  and the microphone converts the waves into an electrical pulse that computers can register. Seismometers also pick up wave activity from deep underground  called seismic waves. These instruments sense it and convert it to a seismograph as seen below.
A seismographs x axis is time, and the y axis is the height of the amplitude of the wave as it moved through the rocky material the seismometer was sitting in. The basic components of a seismic wave on a seismograph is the distanc
The amplitude of the wave can also be large or small based on the material the seismometer is placed in. Bedrock, during an earthquake, doesn't shake as much as sandy or clay soils. Sandy and clay soils tend to magnify the waves as it propagates through the loose material  to whereas solid bed rock tends to minimize the earthquake.
Here is more information on how to interpret and analyze a seismograph from IRIS.
the Richter Scale
The basis of how the Richter scale worked was that for every climb in magnitude, the amplitude of the seismic reading increased 10 fold  hense, it was on a logarithmic scale. What that meant was that every increase in magnitude was an increase of 10x more intense than the last (in terms of all that shaking). However, in terms of energy  every increase of magnitude, was an increase of 32x in terms of energy.
The Moment magnitude & why we no longer use the richter scale
The main reason why we use the moment magnitude scale and no longer use the Richter Scale is:
 The Richter Scale is solely based on the amplitude at a given distance. The problem with that is that the amplitude can be magnified or diminished depending on the material the seismograph is buried in. Mud and loosely consolidated material magnifies the amplitude of the wave  and bedrock diminishes the wave.
 The older styled seismometers didn't pick up all wave frequencies. Now we have electronic seismometers that are much more sensitive to all ranges of frequencies.
 The seismic moment uses more information/variables in its calculations which better reflect the true nature of the factors involved in an earthquake, such as the rocks rigidity  or amount of forces/energy needed to break the rock material, the area that ruptured and the distance it traveled.