Whirlpooling while you chill is essential. I have a whirlpool port, and about 5 minutes before the end of the boil, I start the pump going and begin getting the wort moving. At flameout, I turn on the valve to my chiller (I use a pre-chiller in an ice bath when the tap water temp is too high) and start chilling. At 140F I put the lid on, because below 140F the wort stops creating the DMS precursor, and continue to final temp, usually 65F for most ales, 50F for most lagers (prechiller always used for lagers). Once I'm to pitching temp I turn off the chiller valve, stop the pump, and leave it for 30 minutes to allow all the break material to settle in a cone in the middle. My drain port takes it from the side of the keggle, usually leaving a half-gallon to a gallon of break material behind.
Times vary dramatically depending on temp I'm trying to get to, and temp of tapwater. My city publishes a brewer's water report that includes the average tap water temperature month to month (I live in a brewer's paradise - soft water AND great customer service). This month I expect my 11 gallons of doppelbock will chill to 44F in about 30 minutes.