The starter (which can be an electric motor, hydraulic motor, or most commonly on today's airliners a small compressed-air turbine) couples to the high-pressure compressor by a gear train. Once it spins up to about 10-15% core speed, fuel and ignition are intoduced to the burner. It lights off fairly quickly, and now both the HP turbine and the starter are supplying torque to the compressor to bring it up to an idle speed of 50-65%. Somewhere along the line the starter will cut out automatically, and the HP turbine carries the load at idle and above.
Does this help?