Try to limit wasting actions on movement.
Focus on a balance between preventing outbreaks and curing diseases.
Don't worry too much about eradicating diseases.
Save your event cards for when you really need them, like preventing outbreaks and such.
Build research centers in areas that have lots of connections like Hong Kong, Istanbul, Paris.
Use the Researcher to pass cards more easily. Use the Dispatcher to get the Medic around the board quicker. I love to use the Researcher, Medic, Dispatcher, and Operations Expert in a 4 player game.