In Linde's chaotic model, inflation begins at the Planck time [10^-43]. In other models it begins around the time of the electroweak epoch [10^-36]. In all models it is generally agreed to have ended when the universe was about 10^-32 seconds in age. Bear in mind we still lack any compelling evidence that inflation actually occured, so, it's still just a guess, as Chalnoth pointed out. You will notice all of these 'guess' times coincide with phase transitions in the early universe. At Planck time it is believed the gravitational force had just separated from the primordial super state, when all the known forces in the universe were combined. At the time of the electroweak epoch, the strong nuclear force had just separated from the state known as grand unification, when all the known forces save gravity were still combined.