The Time Phone Booth' travels through the "Circuits of History" to go forwards and backwards in time. It seems to slide along inside the Circuits in a way very analogous to a water-slide (which is undoubtedly why Napoleon Bonaparte was nervous to go into the "Waterloo" slide at first).
The booth uses a directory of numbers called the “Circuits of Time Directory” to guide the boys through their adventure. It probably has the directory, rather than some sort of in-built database, so that the boys can understand how to work it. Each era and location listed on those pages seem to have a 10 to 14 digit dialling code.