There are two basic types of wort chillers, immersion and counter-flow.
The immersion type chiller is submerged into the wort. You then attach the chiller to either a garden hose, or your kitchen faucet (requires the faucet adapter, sold separately). Once attached, you run cold water through the wort chiller and your wort will be at pitching temperature within about fifteen minutes.
Advantages to Immersion Chillers: No need to sanitize! Since you are submerging the chiller in boiling wort, any bacteria present will be killed instantly. When you are finished, be sure to rinse well with hot water.
Easy to use! An immersion chiller is highly recommended for novice to intermediate brewers. No special connections are required, with the exception of the faucet adapter if you are attaching it to your kitchen sink.
The only real disadvantages to using immersion wort chillers are the cooling time and the amount of water used as compared to counter-flow chillers. Still, a quality immersion chiller only takes about fifteen minutes to be effective, and it uses a lot less water than an ice bath.
The counter-flow type has a smaller diameter copper tubing that is inside larger tubing. Wort flows from the kettle through the smaller tube, while cold water flows through the larger tube in the opposite direction. This results in a much shorter cooling time, and you also use less water than with immersion types. Counter-flow wort chillers also require a kettle with a ball valve, and lines for entry and exit.
Advantages to Counter-flow Chillers: FAST! Counter-flow chillers consume the least amount of water and chill at least twice as fast as compared to most immersion types.
Best possible cold break! A counter-flow chiller cools wort to pitching temperatures in minutes, or even seconds! This means that nearly all of the proteins and tannins that may be present will drop out of solution as the wort is chilled and siphoned into the fermenter.
As great as counter-flow chillers are, they do have a few disadvantages. You do need to have enough height difference between kettle and fermenter to allow for a counter-flow chiller. You will need a ball valve on your brew kettle. You will also need to sanitize before and clean after every use.