Each mission has its own specific. For my last mission, we trained for nine months before the actual flight. I started my formal NASA training in 1990. During that period I spent about half of the time in training, the other half I spent performing other duties. I was in training for three years before my first mission, which isn't that long of a wait.
Weightlessness is the fun part of the mission.
There is really nothing to compare it to on Earth. I guess the closest thing would be swimming or scuba diving. It's a similar freedom of movement. What is odd is that weightlessness seems more natural. You don't have the same kinds of sensations in space as you do in the water.