The bottles are ready when they look clear (unless the beer is opaque to begin with, carbonating beer has a sort of hazy look when held up to a bright light), they make a satisfying "pshhh" sound when you pop one open, and they taste good when you drink the beer. Unfortunately, many new brewers have a tendency to bottle "green" beer because they are still familiarizing themselves with proper yeast management and fermentation procedures, which means that you may sometimes experience unbalanced or harsh flavors that will take several weeks or months to age out. So while you are learning, give the beer at least 2-3 weeks in the fermentor and another 3 weeks in the bottle. With more experience, you'll only bottle beers once they are no longer "green", and they'll be ready to drink as soon as they are carbonated, usually within a week or two after bottling, depending on the temperature you keep them at.
The Fiesty(sic) Goat Brewery est. 2007 & Clusterfuggle Experimental Ales est. 2009
Primary: Saison, Berliner Weisse, sLambic I, sLambic II, IPA, 70/-
Secondary: Orange Blossom Mead, Flanders Red I
Kegged: Fat Man Porter w/ 1469, Fat Man Porter w/ 005, Centennial Falcon w/ Conan, Centennial Falcon w/ Denny's, Barrel-aged Fat Man Porter, Belgian Dark Strong, Dark Mild