You start the engine by turning the compressor with a starter. This creates a flow from front of the engine throught the compressor, combustion chamber and turbine to the exhaust. Starter turns the engine to the point where the engine is able to sustain itself.
If you have flow through the compressor, and you have fuel (and ignition or sufficient compression for the fuel to ignite), the turbine will get energy and will be able to run the compressor, which will then be able to "suck" new air from the front of the engine, and so on, and so on.