What are the prerequisites for obtaining a job as a train engineer (driver)? Where could one get training for such a job?

Various union agreements appy differently throughout the US, but I can tell you how it works on the BNSF (Burlington Northern Santa Fe), which is the second largest railraod in the US and operates pretty much everywhere west of the Mississippi River.
One first applies to the position of "Conductor". This is done online via www.bnsf.com They look to hire safety-concious employees with a solid work history. Expect to take lots of drug tests. He or She goes through a training program approx. 4 months long (1/2 classroom and 1/2 on-the-job-training). When this person has enough seniority to bid (apply for) an engine program slot, he or she may do so.
If he or she has enough seniority relative to the pool of bidders, he or she then enters the Engineer Training Program. This lasts about six months (again 1/2 classroom and 1/2 OJT).
However once they turn in their bid to move from conductor to engineer, they are stuck. They must either complete the program and work as an engineer, or quit entirely and surrender their seniority.
Now is an excellent time to hire on with the nation's railroads. For years the railroads hired almost nobody, and that got them into trouble. Now a great percentage of railroad workers are reaching retirement age at the same time.
Before taking a job one should carefully consider the ammount of time that he or she is willing to be away from home. Also, do you mind working nights, weekends, & holidays? Can you stay awake for long periods at odd hours? Can you be '"rested'" even when you don't know when you are going to work? Are you willing to relocate if you suddenly don't have enough seniority to work in your hometown?
It's not all doom&gloom. Railroads pay an excellent salary with good benefits. You get to work outside and see lots of great country. You get to work with a lot of great people.
All in all, it's not a bad place to work.