Transfer the wort from the kettle to the fermenter or a cube (plastic container), then either place in a fridge or just leave at room temperature until the wort has cooled to pitching temperature. This method of chilling has the lowest up-front equipment cost, however the long time taken to cool the wort can result in noticeable DMS.
A coil of copper pipe (commonly called an Immersion Chiller and typically around 15 metres long) connected to hoses at each end is immersed into the kettle at least 10-15 minutes before the end of the boil to sterilise the coil. Once the boil is finished, one hose is connected to a cold water tap, and cold water is passed through the coil to chill the wort while it is still in the kettle. Years ago, copper pipe was cheap, and so this was a cheap and easy way to chill the wort quickly. These days the price of copper has increased dramatically, and so it is no longer cost-effective to buy a new coil of copper pipe. Cheap second-hand coils can still be found occasionally. 18 Meters of copper coil is around the $130 mark.
As an alternative to running lots of tap water through your coil, a reasonably strong pond pump can be immersed in an esky with an ice slurry and used to chill boiling wort in a timely manner. You can conserve a considerable amount of water. However, you will need 3-4 bags of ice and several frozen 2 and 3 litre plastic milk bottles that you can cut open with a Stanley knife and throw in for maximum chilling effect.
A plate chiller (also known as a counter-flow chiller or heat-exchange chiller) is a brick-shaped piece of brewing bling which is attached via hoses between the kettle and the fermenter. As boiling wort from the kettle passes through the plate chiller it is very rapidly chilled by cold water from a tap passing through the chiller in the opposite direction from the wort (the water and wort are kept separate by metal plates inside the chiller). These days the price of plate chillers has come down enough that they can be bought new for less than the price of 15 metres of new copper coil.