One engages in a faulty generalization when the scope of the evidence is too small or the quality of it is too poor to support the conclusion.
In his only trip by car through St. Louis, Joe witnesses the aftermath of the worst car wreck (involving several vehicles and injuries) he's seen in his life. If, upon arriving home, Joe concludes that St. Louis is the most dangerous city in the U.S. in which to drive, he has committed a hasty generalization. In order to justify such a claim, one would probably need to consult reliable, recent data on automobile accident rates in U.S. metropolitan areas.