How does government intervention in market distort market equilibrium?

Whenever the government intervenes in a market it disrupts
market equilibrium in some way.  The exact way that it does this differs depending on
how the government intervenes.

The government can cause
shortages of some commodity by setting a price ceiling for that commodity.  If it does
this, there is more demand than supply at the price the government
orders.

Alternately, the government can cause surpluses by
setting price floors.  An example of this is minimum wage, which causes more people to
want to work compared to how many people employers want to
hire.

Government actions can stimulate or reduce supply (by
taxes or regulations or subsidies) or demand of a product (by changing the amount of
money available) as well.

There are many different ways
that government actions can distort market equilibriums.  But in all cases, the
government's actions do end up either raising or lowering the price and quantity of
goods and services.