The aircraft is accurately aligned E-W in the earth frame and the IRS on its mounting is checked against this alignment to ensure the accuracy of the system/platform interface. The mounting rack is then shimmed to trim out any errors.
It is worth keeping in mind that for current Inertial Systems the aircraft IS the intertial platform (sometimes referred to as a "strap down" system). So, refering to the original question, the IRS is initially aligned to true north and the laser gyros detect rotation rates around the three platform axes. At the same time, accelerometers aligned to the platform axes are detecting rates of change in movement along these axes. All these rates are then integrated in the IRS's digital computer to resolve the changes in roll, pitch and yaw attitude together with the velocity along the axes into a change in position and true heading. True North is not detected once the aircraft is in motion. Current true heading is determined by the detected changes from the initial true heading.