Astronauts do not begin to go through advanced training until they are actually assigned to a crew. This doesn't happen until they have successfully completed the entire one year of classroom work and basic training. Upon completion of all of that, then they officially become astronauts. Astronauts do not begin the advanced training until they are actually assigned to a crew.
Once they begin the advanced training, they spend the majority of their time training on simulators. Astronauts assigned to shuttle missions, for example, will train in the SMS or Shuttle Mission Simulator. These simulators are designed to be capable of reproducing all of the events that are going to take place during the mission. While going through this advanced training, an astronaut may spend as much as eight hours a day training in the simulators.
While they are training in the SMS, they will work with instructors who have come up with a host of problems that are designed to deal with every possible or potential emergency that might arise. They bombard the astronauts with problem after problem, forcing the astronauts to come up with resolutions, all as a means by which to prepare them for real emergencies.
Astronauts will also train by spending time in mock ups. These mock ups are actually life size models of the spacecraft. An astronaut assigned to a shuttle mission will train in a mock up that is an exact replica of the shuttle they will fly in.
The purpose of the training in mock ups is to prepare the astronauts for the close and cramped living and working quarters that they will have to face in the actual spacecraft and on the mission. During these practices, astronauts will do everything from check the equipment, to store supplies and other items or prepare food. They will also use this time to practice the proper way to enter and deplane the space craft.
Another part of advanced training may involve training that isn't necessarily related to the mission proper. As an example, we will use the shuttle mission of 1995 in which American Astronauts went up to the the Russian Mir. One American astronaut was going to be dropped off there and another was to return to Earth. Every astronaut who flew on that mission was required to go through intensive Russian language instruction.
Astronauts who are going to be involved in space walks undergo extensive and intensive training for this. Because water can be used to reproduce the conditions of actual weightlessness, NASA has two training facilities where astronauts can train in water: the WETF is the Weightless Environmental Training Facility and the NBL is the National Buoyancy Lab. In addition, NASA has virtual reality systems that make it possible for astronauts to practice the tasks or chores that they will perform on spacewalks.
Astronauts who may not necessarily be assigned to a crew will go through more training while they wait for a crew assignment. Sometimes new astronauts go on to become experts in some of the support or operational areas. Additionally, sometimes astronauts who aren't involved in mission work at a given time will work on the ground. For this work, they are trained to relay both information and instructions to the astronauts on the spacecraft. The information or instructions may come from engineers, scientists or the flight controllers themselves. Because of this training, astronauts who work on the ground are often able to work with the engineers to solve problems when they arise.
Oberg, James. "Astronaut." World Book Online Reference Center. 2005. World Book, Inc. http://www.worldbookonline.com/wb/Article?id=ar034800 .