Yes, you would start the academy all over again and do all 4 years. Hell, you could be a Dougie Howser (If you don't know who this is, then I'm too old) and finish a master's degree by the time you're 20 years old; and if you went to the air force academy, you'd still have to do 4 years.
As for WHY a person would start one, only to transfer, there is usually one or two reasons.
1. They didn't get their first academy choice, and thought: "No problem. I'll accept this appointment and then simply transfer". Beeep wrong answer. See Flieger's answer.
2. They thought they really wanted a particular academy, then realized that it wasn't what they really wanted. Problem here is; academically, the academies are pretty much the same. There might be a different aura or attitude at each, but it's only 4 years. As Steve mentioned, you would be better off finishing the academy you're at, and then transferring to a different branch of the military. This isn't difficult.