There are many different types of swimming pools, all of varying shapes and sizes. They all have the same basic components however. These are:
The water is pumped in a continuous cycle from the basin through the filter and chemical treatment systems to remove dirt and bacteria from the water. It then reenters the basin and is clean enough to swim in. The water may also be heated to keep it at a required temperature. (used without permission from www.modernpools.com)
The main difference between pools is the basin. These can be above ground, sit in a hole dug in the ground or even float!1. The drains usually sit at the lowest part of the pool and most sinking dirt and debris leave the pool here. Some pools also have drains near the surface which skim off floating debris such as oils and leaves (in outdoor pools).
The pump drives the water from the drains through the filter systems and back into the pool. There is a coarse filter to catch large objects in the water (such as leaves) that may clog up the pump. The water then passes through a finer filter, usually using fine, specialist sand which catches smaller particles in the water. Over time the sand filter can become blocked so it must be backwashed - water is pushed up through the sand to dislodge particles which are then washed into the sewer.
By law all of the water in the pool must pass through the filter in a certain amount of time. This is called the turnover period. The current standard for public pools in Britain is ~2hrs (obviously larger pools will have a slightly longer turnover period)2.
After the filter has removed solid particles, the chemical treatment system then has to remove bacteria and pathogens. This is discussed in more detail in the pages on chlorine and other pool chemicals.