The wort must be cooled rapidly to prevent bacterial growth and to prepare it for the fermentation process. Additionally, cooling the wort is crucial in producing great quality beer as it helps to ensure the beers flavour, aroma and colour are consistent.

After you have completed the boil, the next step is to quickly cool the wort down to a temperature that is suitable to pitch your yeast, typically around 20°C (68°F). Once that the cooling process has begun, everything that now touches the wort should be thoroughly sanitised since bacteria can be introduced to your wort at any temperature below 71°C (160°F).

If the wort is not cooled quickly, off-flavours from oxidation can occur, and you can run the risk of having dimethyl sulphide compounds forming again. Additional organic compounds that contribute to "chill haze" can form if the wort is left to cool too slowly, as well.

After you have removed your wort from the heat source and have completed your hop additions, begin the cooling process by developing a "whirlpool" in the wort. You can do this by simply stirring the wort with a large metal spoon. Whirlpooling is a tactic that most brewers employ to create clear beer. Solid matter (hop trub, small grain particles, etc.) and other proteins will be collected in the centre of the liquid and drop to the bottom of the kettle. This will allow the brewer to avoid siphoning these unwanted organic materials into the fermenter.

Most homebrewers will either use an ice bath to cool their wort or use an immersion chiller or counterflow chiller.

An Ice bath is the lowest maintenance way of cooling your wort. By simply placing your kettle in a large tub with ice and cold water, you can cool your wort to a proper yeast pitching temperature. The drawback to this method is the long lag time to reach the target temperature. 

Immersion chillers are common tools used by homebrewers to cool their wort quicker than the ice bath method. Immersion chillers rely on groundwater flowing through spiral copper tubing that is placed in the wort to chill reach the target temperature. 

Counterflow chillers are designed to exchange heat from cool groundwater flowing through spiral tubes with hot wort that is flowing in the opposite direction of the water in separate spiral tubes. Since the surface contact between the tubes is higher than the amount of surface contact utilised by immersion chillers, counterflow chillers tend to be the most efficient when cooling wort. 

If using a counterflow chiller, the wort will flow directly into the fermenter after being directed through the counterflow chiller. If utilising an immersion chiller or an ice bath (or both, as is common), you'll want to use a sanitised tube to siphon your beer into your sanitised fermenter.