2-3 weeks. A lot depends on the style and if we are talking about a theoretical 'how fast' but typically 3-5 day ferment, 3-5 day dry hop, 1-2 day cold crash and then package. Naturally conditioned beer then wants two weeks from package ideally, but can certainly be done sooner depending on yeast count and viability. Kegs can be force carbed and served immediately, but benefit from being put up to settle for at least 2 days before serving and usually improves with further conditioning time. Some keg beers I serve immediately, but certainly will not be entirely consumed immediately, still it is tapped 7-12 days from mashing in.
Usual method for me is to pitch enough yeast to get me about done for an average wort in 3 days. I dry hop at that point, usually with a point or two remaining, seal and roll my vessel. I roll it again to suspend the hops on the first, second and third days allowing fermentation to completely finish venting if necessary and then chill on the evening of the sixth. I tend to give it 1-2 days cold crash before kegging sometime on the eighth day.
At the moment I've been priming kegs with a sugar because it is very warm. Saves some co2 and the beer warms up and conditions quickly in this heat. In the winter tend to force carb as the beer comes off the cold crash close to 0C, takes ages to warm up and condition at room temperature.