How long should a grow take from when it sprouts to harvest? Is there a set time? What would make the grow complete faster?
It is not a set time, unless you're using an autoflower plant. Those grows usually take around 60 days. Otherwise, it's dependant on how long you veg the plant for. Read the stickies for more information (stickies are posts at the top of the forums).
60 days is about the length of flowering time, though that depends on strain/genetics. You veg for as long as you want before that, the longer you veg the more you grow out your plant and, generally, the larger your yield.