A market is defined as a place where a group of buyers and sellers interact with each other for the purpose of buying and selling a particular good or service.
Price will adjust until quantity demanded equals quantity supplied, this is known as equilibrium price and quantity, market price or market clearing price.
There are four possibilities in which market prices can respond to changes in either demand and supply: increase in demand, decrease in demand, increase in supply, and decrease in supply.
The effect of a Price Ceiling on consumer and producer surplus is that price falls so producer surplus falls and consumer surplus increases, but both the consumer and producer lose as there is deadweight loss.
To solve for equilibrium price and quantity, write equation so they both equal, set Qs (quantity supplied) equal to Qd (quantity demanded), solve for P, this is going to be your equilibrium Price for the problem, and then plug your equilibrium price into either your demand or supply function (or both--but most times it will be easier to plug into supply) and solve for Q, which will give you equilibrium quantity.
The effect of a Price Floor on consumer and producer surplus is that price increases so consumer surplus falls and producer surplus increases, but both the consumer and producer lose as there is deadweight loss.