What do I need to power up an EDF engine?
An EDF is an electric ducted fan, so I assume you're not interested in the fans powered by internal combustion engines (or actual turbines).

You'll need: 


an ESC (electronic speed controller) that is rated for at least the maximum current and voltage of the motor in the EDF.  
a battery that can provide that current and voltage.
something to provide a throttle signal to the ESC. Usually this is a transmitter and receiver, but for bench-testing a simple, cheap option is a servo tester.
a charger for the battery. This must be able to match the battery chemistry, voltage and capacity (they normally handle a range)
if the charger isn't mains powered, it will need a power supply.


There are loads of on-line shops for all this.