First you need to know what a CSI is. The tv show combines several aspects of Crime Scene Investigators, Latent Print Examiners, Forensic Scientists, and etc..
Real Crime Scene Investigators go to crime scenes to document the scene, collect evidence, and then enter that evidence into the property room. The evidence is then analyzed by forensic scientists and processed for more evidence (latent prints or trace evidence).
Certainly, some agencies have people that perform many of the functions described, but the person acting only as a CSI, does just crime scene work.
A CSI needs to be able to process objects and locations for latent fingerprints, operate alternate light sources, photograph scenes, be able to draw/sketch accurately, and write a descriptive report of what was seen and collected.
So a college education to be a CSI must include photography (emphasis on macro), technical writing, basic drafting, some forensics classes, and more.
One aspect of this is that many agencies have commissioned police officers performing CSI duties. This would mean that you'd have to be a police officer before you could become a CSI.
Hope this helps.